{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Arial Narrow" 1 12 128 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2d input" -1 256 "Arial Narrow" 0 0 0 0 255 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "Helvetica" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 268 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 286 "Courier" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE " " -1 289 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 290 " " 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 291 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 292 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 293 "Courier" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 294 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 295 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 296 "Helvetica" 0 1 0 128 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 297 "Helvetica" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 298 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 300 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 301 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 302 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 303 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 304 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 305 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 306 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 307 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 308 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 309 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 310 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 311 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 312 "Times " 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 313 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 314 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 315 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 316 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 317 "Helvetica" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 318 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 319 "" 0 1 0 0 64 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 320 "Helvetica" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 321 " " 0 1 111 0 7 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 322 "" 0 1 111 0 7 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 323 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 324 "Courier" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 325 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 326 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 327 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 328 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 329 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 330 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 331 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 332 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 333 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 334 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 335 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 336 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 337 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 338 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 339 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 340 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 } {CSTYLE "" -1 341 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 342 "Courier" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 343 "H elvetica" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 344 "Helvetic a" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 345 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 346 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 347 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 348 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 349 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 350 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 351 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 352 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 353 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 354 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 355 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 356 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 357 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 358 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 359 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 360 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 361 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 362 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 363 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 364 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 365 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 366 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 367 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 368 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 369 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 370 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 371 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 372 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 373 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 374 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 375 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 376 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 377 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 378 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 379 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 380 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 381 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 382 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 383 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 384 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 385 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 386 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 387 "" 0 1 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 388 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Arial Narrow" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output " -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 3 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Arial Narrow" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Arial Narrow" 1 12 128 0 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier " 1 12 0 128 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Arial Narrow" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 259 1 {CSTYLE "" -1 -1 "Arial Narrow" 1 12 0 0 0 1 1 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 317 39 "MATRICES AND MATRIX OPE RATIONS: Unit 26" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{PARA 258 "" 0 "" {TEXT 319 23 "Dr. Wlodzislaw Kostecki" }}{PARA 259 "" 0 " " {TEXT -1 53 "The Papua New Guinea University of Technology (PNGUT)" }}{PARA 259 "" 0 "" {TEXT -1 54 "Department of Electrical and Communic ation Engineering" }}{PARA 259 "" 0 "" {TEXT -1 20 "Lae, Morobe Provin ce" }}{PARA 259 "" 0 "" {TEXT -1 16 "Papua New Guinea" }}{PARA 2 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 318 41 "Copyright \251 200 0 by Wlodzislaw Kostecki" }}{PARA 258 "" 0 "" {TEXT 320 19 "All right s reserved" }}{PARA 2 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 321 67 "-------------------------------------------------------------- -----" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 257 4 "(26)" }{TEXT 297 1 " " }{TEXT 296 38 "Applying a functi on to matrix elements" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 343 10 "OBJECTIVES" }{TEXT 344 1 ":" }}} {EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 345 1 "\225" }{TEXT -1 66 " To provide alternative methods of applica tion of a function to " }{TEXT 350 4 "each" }{TEXT -1 22 " element o f a matrix." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 346 1 "\225" }{TEXT -1 66 " To provide alternative methods of application of a function to \+ " }{TEXT 351 8 "selected" }{TEXT -1 23 " elements of a matrix." }}} {EXCHG {PARA 0 "" 0 "" {TEXT 347 1 "\225" }{TEXT -1 90 " To provide e xamples of application of some common functions to constant-matrix ele ments." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 348 1 "\225" }{TEXT -1 26 " T o show how to suppress " }{TEXT 355 5 "Maple" }{TEXT 354 1 "\222" } {TEXT -1 132 "s internal evaluation of matrix elements upon applicatio n of a function if the textbook form of display of such a matrix is de sired." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 349 1 "\225" }{TEXT -1 100 " \+ To show how to perform exact and floating-point evaluation of a matrix that has been entered with " }{TEXT 353 5 "Maple" }{TEXT 352 1 "\222 " }{TEXT -1 33 "s internal evaluation suppressed." }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "rest art : with(linalg, coldim, diag, rowdim) :" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "There are thre e alternative methods of applying a function to each element of a matr ix. One method uses the " }{TEXT 356 5 "evalm" }{TEXT -1 37 " function and two methods employ the " }{TEXT 259 3 "map" }{TEXT -1 10 " functi on." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 25 "For example, consider a " }{TEXT 311 1 "(" }{XPPEDIT 18 0 "2" "6#\"\"#" }{TEXT 312 3 " \327 " }{XPPEDIT 18 0 "3" "6#\"\"$" }{TEXT 313 1 ")" }{TEXT -1 10 " matrix [" }{TEXT 284 1 "A" }{TEXT -1 1 "]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "A := matrix(2, 3, [ a[11], a[12], a[13], a[21], a[22], a[23]]) : A = matrix(A) ;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"AG-%'matrixG6#7$7%&%\"aG6#\"#6&F+6 #\"#7&F+6#\"#87%&F+6#\"#@&F+6#\"#A&F+6#\"#B" }}}{EXCHG {PARA 2 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "and obtain a ma trix whose elements are equal to the " }{TEXT 292 6 "cosine" }{TEXT -1 22 " of the elements of [" }{TEXT 285 1 "A" }{TEXT -1 2 "]." }}} {EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "This may be done using any of the following alternative methods ." }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 357 8 "Method 1" }{TEXT -1 12 ". Using the " }{TEXT 358 5 "evalm " }{TEXT -1 10 " function:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "A_cos := evalm(cos(A)) : A_cos = matrix(A_cos) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&A_cosG-%'matrixG6#7$7%-%$cosG6#&%\"aG6#\"#6-F+6 #&F.6#\"#7-F+6#&F.6#\"#87%-F+6#&F.6#\"#@-F+6#&F.6#\"#A-F+6#&F.6#\"#B" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 300 8 "Method 2" }{TEXT -1 12 ". Using the " }{TEXT 301 3 "map" }{TEXT -1 10 " function:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "A_cos := map(cos, A) : A_cos = matrix(A_cos) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&A_cosG-%'matrixG6#7$7%-%$cosG6#&%\"aG6#\"#6-F+6#&F.6 #\"#7-F+6#&F.6#\"#87%-F+6#&F.6#\"#@-F+6#&F.6#\"#A-F+6#&F.6#\"#B" }}} {EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 340 8 "Method 3" }{TEXT -1 21 ". Using the function " }{TEXT 339 3 "ma p" }{TEXT -1 40 " together with the arrow-type procedure:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "A_cos := map(x->cos(x), A) : A_co s = matrix(A_cos) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&A_cosG-%'mat rixG6#7$7%-%$cosG6#&%\"aG6#\"#6-F+6#&F.6#\"#7-F+6#&F.6#\"#87%-F+6#&F.6 #\"#@-F+6#&F.6#\"#A-F+6#&F.6#\"#B" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 286 5 "* * *" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 287 4 "N.B." } {TEXT -1 33 " If a function is to be applied " }{TEXT 295 4 "only" } {TEXT -1 5 " to " }{TEXT 366 8 "selected" }{TEXT -1 200 " elements o f a matrix, inputting of such a matrix requires application of the fun ction individually to each of the elements chosen. This can be done us ing either of the following alternative methods." }}}{EXCHG {PARA 2 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 302 8 "Method 1" }{TEXT -1 10 ". Use the " }{TEXT 303 4 "subs" }{TEXT -1 59 " function \+ to substitute the selected matrix elements with " }{TEXT 310 6 "cosin e" }{TEXT -1 20 " of these elements." }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "For example, appl y the function " }{TEXT 290 6 "cosine" }{TEXT -1 19 " to the element s " }{XPPEDIT 18 0 "a[11]" "6#&%\"aG6#\"#6" }{TEXT 288 1 "," }{TEXT -1 2 " " }{XPPEDIT 18 0 "a[13]" "6#&%\"aG6#\"#8" }{TEXT 289 1 "," } {TEXT -1 7 " and " }{XPPEDIT 18 0 "a[22]" "6#&%\"aG6#\"#A" }{TEXT -1 22 " of the same matrix [" }{TEXT 291 1 "A" }{TEXT -1 2 "]." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "A_cos_select := subs(A[1,1]= cos(A[1,1]), A[1,3]=cos(A[1,3]), A[2,2]=cos(A[2,2]), matrix(A)) :" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A_cos_select = matrix(A_cos_ select) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%-A_cos_selectG-%'matrix G6#7$7%-%$cosG6#&%\"aG6#\"#6&F.6#\"#7-F+6#&F.6#\"#87%&F.6#\"#@-F+6#&F. 6#\"#A&F.6#\"#B" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 308 8 "Method 2" }{TEXT -1 62 ". Specify the sel ected matrix elements to which the function " }{TEXT 304 6 "cosine" } {TEXT -1 43 " is to be applied and evaluate the matrix." }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "F or example, apply the function " }{TEXT 306 6 "cosine" }{TEXT -1 19 " to the elements " }{XPPEDIT 18 0 "a[12]" "6#&%\"aG6#\"#7" }{TEXT 309 1 "," }{TEXT -1 2 " " }{XPPEDIT 18 0 "a[21]" "6#&%\"aG6#\"#@" } {TEXT 305 1 "," }{TEXT -1 7 " and " }{XPPEDIT 18 0 "a[23]" "6#&%\"aG 6#\"#B" }{TEXT -1 22 " of the same matrix [" }{TEXT 307 1 "A" }{TEXT -1 2 "]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "A[1,2] := cos(A [1,2]) : A[2,1] := cos(A[2,1]) : A[2,3] := cos(A[2,3]) :" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "A_cos_select := eval(A) : \+ A_cos_select = matrix(A_cos_select) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%-A_cos_selectG-%'matrixG6#7$7%&%\"aG6#\"#6-%$cosG6#&F+6#\"#7&F+6# \"#87%-F/6#&F+6#\"#@&F+6#\"#A-F/6#&F+6#\"#B" }}}{EXCHG {PARA 2 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 293 5 "* * *" }}} {EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 325 4 "N.B." }{TEXT -1 120 " If a function is to be applied to diagon al elements of a diagonal matrix, either of the following methods may \+ be used." }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 31 "For example, apply a function " }{TEXT 333 1 "f" }{TEXT -1 33 " to the diagonal elements of a " }{TEXT 327 1 "(" } {XPPEDIT 18 0 "4" "6#\"\"%" }{TEXT 328 3 " \327 " }{XPPEDIT 18 0 "4" " 6#\"\"%" }{TEXT 329 1 ")" }{TEXT -1 19 " diagonal matrix [" }{TEXT 326 1 "A" }{TEXT -1 10 "] given as" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "A := diag(a[11], a[22], a[33], a[44]) : A = matrix( A) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"AG-%'matrixG6#7&7&&%\"aG6# \"#6\"\"!F.F.7&F.&F+6#\"#AF.F.7&F.F.&F+6#\"#LF.7&F.F.F.&F+6#\"#W" }}} {EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 332 8 "Method 1" }{TEXT -1 12 ". Using the " }{TEXT 331 5 "array" } {TEXT -1 28 " function together with the " }{TEXT 330 8 "diagonal" } {TEXT -1 19 " indexing function:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "A_f := array(diagonal, 1..4, 1..4, [(1,1)=f(A[1,1]), (2,2)=f(A[2,2]), (3,3)=f(A[3,3]), (4,4)=f(A[4,4])]) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A_f = matrix(A_f) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%$A_fG-%'matrixG6#7&7&-%\"fG6#&%\"aG6#\"#6\"\"!F1 F17&F1-F+6#&F.6#\"#AF1F17&F1F1-F+6#&F.6#\"#LF17&F1F1F1-F+6#&F.6#\"#W" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 334 8 "Method 2" }{TEXT -1 19 ". Using the double " }{TEXT 335 3 "for" }{TEXT -1 16 "-loop construct:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "a_f := array(diagonal, 1..rowdim(A), 1..coldim(A)) : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "for i to rowdim(A) do \+ for j to coldim(A) do if j = i then a_f[i,j] := f(A[i,j]) fi : od : od :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "A_f := matrix( a_f) : A_f = matrix(A_f) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%$A_f G-%'matrixG6#7&7&-%\"fG6#&%\"aG6#\"#6\"\"!F1F17&F1-F+6#&F.6#\"#AF1F17& F1F1-F+6#&F.6#\"#LF17&F1F1F1-F+6#&F.6#\"#W" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 336 4 "N.B." }{TEXT -1 54 " The construction of this method is such that it has " }{TEXT 338 2 "no" }{TEXT -1 12 " effect on [" }{TEXT 337 1 "A" }{TEXT -1 74 " ] in view of a possible need for using the matrix in further computati ons." }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 324 5 "* * *" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "For the purposes of numerical exam ples of application of functions to " }{TEXT 294 3 "all" }{TEXT -1 36 " elements of a matrix, consider a " }{TEXT 314 1 "(" }{XPPEDIT 18 0 "2" "6#\"\"#" }{TEXT 315 3 " \327 " }{XPPEDIT 18 0 "3" "6#\"\"$" }{TEXT 316 1 ")" }{TEXT -1 10 " matrix [" }{TEXT 258 1 "A" }{TEXT -1 10 "] given as" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "A := matr ix(2, 3, [-2, 3, 1, 5, 2, 4]) : A = matrix(A) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"AG-%'matrixG6#7$7%!\"#\"\"$\"\"\"7%\"\"&\"\"#\"\"% " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Apply the following functions to the matrix elements and \+ compute their values." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "(a) Apply the " }{TEXT 261 11 "ex ponential" }{TEXT -1 38 " function to each element of matrix [" } {TEXT 275 1 "A" }{TEXT -1 1 "]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "A_exp := map(exp, A) : A_exp = matrix(A_exp) ;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/%&A_expG-%'matrixG6#7$7%-%$expG6#!\"#-F+6#\"\"$ -F+6#\"\"\"7%-F+6#\"\"&-F+6#\"\"#-F+6#\"\"%" }}}{EXCHG {PARA 2 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "or, using the \+ " }{TEXT 269 5 "evalm" }{TEXT -1 10 " function," }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 50 "A_exp := evalm(exp(A)) : A_exp = matrix(A_ex p) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&A_expG-%'matrixG6#7$7%-%$ex pG6#!\"#-F+6#\"\"$-F+6#\"\"\"7%-F+6#\"\"&-F+6#\"\"#-F+6#\"\"%" }}} {EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Floating-point evaluation of the above " }{TEXT 260 5 "exact" } {TEXT -1 35 " result gives the following matrix:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "A_exp := evalf(matrix(A_exp)) : A_exp = mat rix(A_exp) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&A_expG-%'matrixG6#7 $7%$\"+KGN`8!#5$\"+#p`&3?!\")$\"+G=G=F!\"*7%$\"+\"fJT[\"!\"($\"+*4c!*Q (F2$\"+.]\")faF/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "(b) Apply the function " }{TEXT 262 17 " natural logarithm" }{TEXT -1 29 " to each element of matrix [" } {TEXT 276 1 "A" }{TEXT -1 1 "]" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 360 4 "N.B." }{TEXT -1 53 " Upon ap plication of a function to matrix elements, " }{TEXT 359 5 "Maple" } {TEXT -1 25 " computes internally the " }{TEXT 361 5 "exact" }{TEXT -1 134 " values of new matrix elements and displays them in this form. If it is required to display the new elements in the unevaluated form " }{TEXT 363 1 "f" }{TEXT 364 19 "(original element)," }{TEXT -1 110 " a proper use of single quotes will prevent internal evaluation. This is illustrated below for the function " }{TEXT 365 17 "natural \+ logarithm" }{TEXT -1 37 " applied to the elements of matrix [" } {TEXT 362 1 "A" }{TEXT -1 2 "]." }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "A_ln := map('('ln', A) ') : A_ln = matrix(A_ln) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%A_l nG-%'matrixG6#7$7%-%#lnG6#!\"#-F+6#\"\"$-F+6#\"\"\"7%-F+6#\"\"&-F+6#\" \"#-F+6#\"\"%" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 380 4 "N.B." }{TEXT -1 71 " It may be easily no ticed that evaluation of the element at location " }{TEXT 381 5 "(1,1 )" }{TEXT -1 15 " will give a " }{TEXT 382 7 "complex" }{TEXT -1 66 " number. Therefore, evaluation of the above matrix will yield a " } {TEXT 383 7 "complex" }{TEXT -1 72 " matrix. The exact evaluation may be done by using either the function " }{TEXT 384 5 "evalc" }{TEXT -1 88 ", which is specifically designed to evaluate complex-valued exp ressions or the function " }{TEXT 385 4 "eval" }{TEXT -1 1 "." }}} {EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 379 8 "Method 1" }{TEXT -1 21 ". Using the function " }{TEXT 377 3 "ma p" }{TEXT -1 59 " together with the arrow-type procedure including fun ction " }{TEXT 378 5 "evalc" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "A_ln = map(x->evalc(x), A_ln) ;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/%%A_lnG-%'matrixG6#7$7%,&-%#lnG6#\"\"#\"\"\"*&^#F/F/ %#PiGF/F/-F,6#\"\"$\"\"!7%-F,6#\"\"&F+-F,6#\"\"%" }}}{EXCHG {PARA 2 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 388 8 "Method 2" }{TEXT -1 21 ". Using the function " }{TEXT 386 3 "map" }{TEXT -1 59 " together with the arrow-type procedure including function " }{TEXT 387 4 "eval" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "A_ln := map(x->eval(x), A_ln) : A_ln = matrix(A_ln) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%A_lnG-%'matrixG6#7$7%,&-%#lnG6#\"\"#\"\" \"*&^#F/F/%#PiGF/F/-F,6#\"\"$\"\"!7%-F,6#\"\"&F+-F,6#\"\"%" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "F loating-point evaluation yields" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "A_ln := evalf(matrix(A_ln)) : A_ln = matrix(A_ln) ;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/%%A_lnG-%'matrixG6#7$7%^$$\"+1=ZJp!#5 $\"+aEfTJ!\"*$\"+*G7')4\"F0$\"\"!F47%$\"+7zV4;F0F+$\"+hVH'Q\"F0" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "(c) Apply the " }{TEXT 263 13 "trigonometric" }{TEXT -1 12 " \+ function " }{TEXT 264 4 "sine" }{TEXT -1 29 " to each element of mat rix [" }{TEXT 277 1 "A" }{TEXT -1 1 "]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "A_sin := map(sin, A) : A_sin = matrix(A_sin) ;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/%&A_sinG-%'matrixG6#7$7%,$-%$sinG6#\" \"#!\"\"-F,6#\"\"$-F,6#\"\"\"7%-F,6#\"\"&F+-F,6#\"\"%" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "o r, as a floating-point approximation," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "A_sin := evalf(matrix(A_sin)) : A_sin = matrix(A_si n) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&A_sinG-%'matrixG6#7$7%$!+oU (H4*!#5$\"+\"3+7T\"F,$\"+[)4ZT)F,7%$!+ZFC*e*F,$\"+oU(H4*F,$!+`\\-ovF, " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "(d) Apply the " }{TEXT 265 21 "inverse trigonometric" } {TEXT -1 12 " function " }{TEXT 266 11 "arc tangent" }{TEXT -1 29 " \+ to each element of matrix [" }{TEXT 278 1 "A" }{TEXT -1 1 "]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "A_arctan := map('('arctan', \+ A)') : A_arctan = matrix(A_arctan) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%)A_arctanG-%'matrixG6#7$7%-%'arctanG6#!\"#-F+6#\"\"$-F+6#\"\" \"7%-F+6#\"\"&-F+6#\"\"#-F+6#\"\"%" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Exact evaluation of the above matrix yields" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "A_a rctan := map(x->eval(x), A_arctan) : A_arctan = matrix(A_arctan) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%)A_arctanG-%'matrixG6#7$7%,$-%'arc tanG6#\"\"#!\"\"-F,6#\"\"$,$%#PiG#\"\"\"\"\"%7%-F,6#\"\"&F+-F,6#F7" }} }{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Floating-point evaluation yields" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "A_arctan := evalf(matrix(A_arctan)) : A_arctan = ma trix(A_arctan) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%)A_arctanG-%'mat rixG6#7$7%$!+=([r5\"!\"*$\"+sd/\\7F,$\"+N;)R&y!#57%$\"+n2St8F,$\"+=([r 5\"F,$\"+kw\"eK\"F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "(e) Apply the " }{TEXT 270 10 "hy perbolic" }{TEXT -1 12 " function " }{TEXT 271 15 "hyperbolic sine" }{TEXT -1 29 " to each element of matrix [" }{TEXT 279 1 "A" }{TEXT -1 1 "]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "A_sinh := map(si nh, A) : A_sinh = matrix(A_sinh) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/%'A_sinhG-%'matrixG6#7$7%,$-%%sinhG6#\"\"#!\"\"-F,6#\"\"$-F,6#\"\" \"7%-F,6#\"\"&F+-F,6#\"\"%" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "or, as a floating-point approxima tion," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "A_sinh := evalf(ma trix(A_sinh)) : A_sinh = matrix(A_sinh) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'A_sinhG-%'matrixG6#7$7%$!+3/'oi$!\"*$\"+$\\(y,5!\")$ \"+%>,_<\"F,7%$\"+e5K?uF/$\"+3/'oi$F,$\"+?<**GFF/" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "(f) Apply \+ the " }{TEXT 272 18 "inverse hyperbolic" }{TEXT -1 12 " function " }{TEXT 273 23 "inverse hyperbolic sine" }{TEXT -1 29 " to each elemen t of matrix [" }{TEXT 280 1 "A" }{TEXT -1 1 "]" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 70 "A_arcsinh := map('('arcsinh', A)') : A_arcsi nh = matrix(A_arcsinh) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*A_arcsi nhG-%'matrixG6#7$7%-%(arcsinhG6#!\"#-F+6#\"\"$-F+6#\"\"\"7%-F+6#\"\"&- F+6#\"\"#-F+6#\"\"%" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Exact evaluation of the above matr ix yields" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "A_arcsinh := m ap(x->eval(x), A_arcsinh) : A_arcsinh = matrix(A_arcsinh) ;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/%*A_arcsinhG-%'matrixG6#7$7%,$-%(arcs inhG6#\"\"#!\"\"-F,6#\"\"$-%#lnG6#,&\"\"\"F7*$-%%sqrtG6#F.F7F77%-F,6# \"\"&F+-F,6#\"\"%" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Floating-point evaluation yields" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "A_arcsinh := evalf(matrix(A_ arcsinh)) : A_arcsinh = matrix(A_arcsinh) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*A_arcsinhG-%'matrixG6#7$7%$!+vajV9!\"*$\"+fkW==F,$\" +pet8))!#57%$\"+T$QCJ#F,$\"+vajV9F,$\"+ZDr%4#F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "(g) Apply th e " }{TEXT 267 11 "square root" }{TEXT -1 38 " function to each elem ent of matrix [" }{TEXT 281 1 "A" }{TEXT -1 1 "]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "A_sqrt := map(sqrt, A) : A_sqrt = matrix(A_ sqrt) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'A_sqrtG-%'matrixG6#7$7%* &^#\"\"\"F,-%%sqrtG6#\"\"#F,*$-F.6#\"\"$F,F,7%*$-F.6#\"\"&F,*$F-F,F0" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "or, as a floating-point approximation," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "A_sqrt := evalf(matrix(A_sqrt)) : A_sqr t = matrix(A_sqrt) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'A_sqrtG-%'m atrixG6#7$7%^#$\"+iN@99!\"*$\"+330K " 0 "" {MPLTEXT 1 0 76 "`A_pwr(2/3)` := map(x->x^(2/3), A) : A_pwr(`2/3`) = matrix(`A_pwr(2/3)`) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&A_pwrG6 #%$2/3G-%'matrixG6#7$7%*$)!\"##\"\"#\"\"$\"\"\"*$)F2F0F3F37%*$)\"\"&F0 F3*$)F1F0F3*$)\"\"%F0F3" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Since evaluation of the element at location " }{TEXT 372 5 "(1,1)" }{TEXT -1 15 " will give a " } {TEXT 373 7 "complex" }{TEXT -1 86 " number, a further evaluation of \+ the above matrix may be tried by using the function " }{TEXT 374 3 "ma p" }{TEXT -1 59 " together with the arrow-type procedure including fun ction " }{TEXT 375 5 "evalc" }{TEXT -1 29 ". This yields the following " }{TEXT 376 7 "complex" }{TEXT -1 9 " matrix:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 88 "`A_pwr(2/3)` := map(x->evalc(x), `A_pwr(2/3) `) : A_pwr(`2/3`) = matrix(`A_pwr(2/3)`) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&A_pwrG6#%$2/3G-%'matrixG6#7$7%,&*$)\"\"##F0\"\"$\" \"\"#!\"\"F0*(^##F3F0F3F/F3-%%sqrtG6#F2F3F3*$)F2F1F3F37%*$)\"\"&F1F3F. *$)\"\"%F1F3" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Floating-point evaluation yields" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "`A_pwr(2/3)` := evalf(matrix(`A_pwr (2/3)`)) : A_pwr(`2/3`) = matrix(`A_pwr(2/3)`) ;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/-%&A_pwrG6#%$2/3G-%'matrixG6#7$7%^$$!+g_+Pz!#5$\"+Q' HZP\"!\"*$\"+BQ3!3#F3$\"\"\"\"\"!7%$\"+Qx,CHF3$\"+_5S(e\"F3$\"++@%)>DF 3" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "(h) Apply a " }{TEXT 274 28 "negative fractional exponen t" }{TEXT -1 7 " of \226" }{XPPEDIT 18 0 "2" "6#\"\"#" }{TEXT -1 3 " / " }{XPPEDIT 18 0 "5" "6#\"\"&" }{TEXT -1 29 " to each element of m atrix [" }{TEXT 283 1 "A" }{TEXT -1 1 "]" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "To display this o peration in \"like-in-a-book\" form, suppress " }{TEXT 298 5 "Maple" } {TEXT 341 1 "\222" }{TEXT -1 33 "s internal evaluation as follows:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "`A_pwr(-2/5)` := map(x->x^( `-2/5`), A) : A_pwr(`-2/5`) = matrix(`A_pwr(-2/5)`) ;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/-%&A_pwrG6#%%-2/5G-%'matrixG6#7$7%)!\"#F')\"\"$ F'\"\"\"7%)\"\"&F')\"\"#F')\"\"%F'" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Normally, " }{TEXT 299 5 "Maple" }{TEXT -1 73 " makes internal evaluation and displays the re sult in the following form:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "`A_pwr(-2/5)` := map(x->x^(-2/5), A) : A_pwr(`-2/5`) = matrix(`A _pwr(-2/5)`) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&A_pwrG6#%%-2/5G- %'matrixG6#7$7%,$*$)!\"##\"\"$\"\"&\"\"\"#!\"\"\"\"#,$*$)F2F1F4#F4F2F4 7%,$*$)F3F1F4#F4F3,$*$)F7F1F4#F4F7,$*$)\"\"%F1F4#F4FH" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "S ince evaluation of the element at location " }{TEXT 367 5 "(1,1)" } {TEXT -1 15 " will give a " }{TEXT 368 7 "complex" }{TEXT -1 86 " n umber, a further evaluation of the above matrix may be tried by using \+ the function " }{TEXT 369 3 "map" }{TEXT -1 59 " together with the arr ow-type procedure including function " }{TEXT 370 5 "evalc" }{TEXT -1 29 ". This yields the following " }{TEXT 371 7 "complex" }{TEXT -1 9 " matrix:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "`A_pwr(-2/5)` := map(x->evalc(x), `A_pwr(-2/5)`) : A_pwr(`-2/5`) = matrix(`A_pwr( -2/5)`) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&A_pwrG6#%%-2/5G-%'mat rixG6#7$7%,&*&)\"\"##\"\"$\"\"&\"\"\"-%$cosG6#,$%#PiG#F0F3F4#F4F0*(^## !\"\"F0F4F/F4-%$sinGF7F4F4,$*$)F2F1F4#F4F2F47%,$*$)F3F1F4#F4F3,$*$F/F4 F;,$*$)\"\"%F1F4#F4FP" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Floating-point evaluation yields" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "`A_pwr(-2/5)` := evalf(ma trix(`A_pwr(-2/5)`)) : A_pwr(`-2/5`) = matrix(`A_pwr(-2/5)`) ;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&A_pwrG6#%%-2/5G-%'matrixG6#7$7%^$$ \"+&)3\">M#!#5$!+!fgw?(F0$\"+\\,%RW'F0$\"\"\"\"\"!7%$\"+3c0`_F0$\"+NGe yvF0$\"+v<\\VdF0" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 342 5 "* * *" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Proceed to Unit (27) fo r \"" }{TEXT 323 48 "Differentiation of matrices comprising functions " }{TEXT -1 2 "\"." }}}{EXCHG {PARA 258 "" 0 "" {TEXT 322 67 "-------- -----------------------------------------------------------" }}}} {MARK "63 0 0" 0 }{VIEWOPTS 0 0 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }