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482 Matrices
Hessenberg Matrix reduction to Hessenberg form. Returns [P,B] such
that B=inv(P)*A*P.
hessenberg(Mtrx(A))
Example:
In CAS view, hessenberg
returns
Smith Smith normal form of a matrix with coefficients in Z:
returns U,B,V such that U and V invertible in Z, B is
diagonal, B[i,i] divides B[i+1,i+1], and B=U*A*V.
ismith(Mtrx(A))
Example:
ismith returns
123
456
789
100
0
4
7
-1
010
1
29
7
---2 7
39
7
---8 0
278
49
-----
3
7
-
123
456
789
100
41– 0
1– 21–
100
030
000
12– 1
01 2–
00 1
- HP Prime Graphing Calculator 1
- User Guide 1
- Edition1 2
- Part Number NW280-2001 2
- Legal Notices 2
- Printing History 3
- Contents 5
- 4 Exam Mode 6
- 5 An introduction to HP apps 6
- 6 Function app 7
- 7 Advanced Graphing app 7
- 8Geometry 7
- 9 Spreadsheet 7
- 10 Statistics 1Var app 7
- 11 Statistics 2Var app 8
- 12 Inference app 8
- 13 Solve app 8
- 14 Linear Solver app 8
- Contents 5 9
- 22 Variables 10
- 23 Units and constants 10
- 24 Lists 11
- 25 Matrices 11
- 26 Notes and Info 11
- 27 Programming in HP PPL 11
- 28 Basic integer arithmetic 12
- A Glossary 12
- B Troubleshooting 12
- Manual conventions 13
- =, \, >, and < 14
- Getting started 15
- On/off, cancel operations 16
- The display 17
- Sections of the display 18
- [orange] In Home view 19
- Navigation 20
- Touch gestures 21
- The keyboard 22
- Context-sensitive menu 23
- Entry and edit keys 24
- Keys Purpose (Continued) 25
- Shift keys 26
- Adding text 27
- Math keys 28
- Getting started 25 29
- Hexagesimal 30
- EEX key 31
- (powers of 31
- E15. This is 32
- Input forms 33
- System-wide settings 34
- Setting Options 35
- Textbook: An expression is 36
- Algebraic: An expression is 36
- Math and CAS 37
- Setting Options (Continued) 38
- Specifying a Home setting 39
- Mathematical calculations 40
- Entering expressions 41
- Example Calculate 42
- Negative 43
- Explicit and 44
- Getting started 41 45
- Storing a value in a variable 46
- Example: To assign 47
- Complex numbers 48
- Sharing data 48
- Getting started 45 49
- Online Help 50
- Reverse Polish Notation (RPN) 51
- History in RPN mode 52
- Sample calculations 53
- Manipulating the stack 55
- Before After 56
- Computer algebra system (CAS) 57
- CAS calculations 58
- Setting Purpose 60
- 60
- Setting Purpose (Cont.) 61
- Exam Mode 65
- O + A + c 66
- Creating a new configuration 67
- Activating Exam Mode 68
- SH, tap 69
- Modifying configurations 70
- Deleting configurations 71
- 68 Exam Mode 72
- An introduction to HP apps 73
- 70 An introduction to HP apps 74
- Application Library 75
- To delete an 76
- App views 77
- Symbolic Setup view 78
- Plot view 79
- Numeric view 81
- Numeric Setup view 82
- Quick example 83
- RNG field to 84
- An introduction to HP apps 81 85
- 82 An introduction to HP apps 86
- An introduction to HP apps 83 87
- 84 An introduction to HP apps 88
- An introduction to HP apps 85 89
- Button Purpose 90
- SY to open Symbolic 91
- 88 An introduction to HP apps 92
- Option Result 93
- XRNG and YRNG 94
- An introduction to HP apps 91 95
- 92 An introduction to HP apps 96
- An introduction to HP apps 93 97
- 94 An introduction to HP apps 98
- An introduction to HP apps 95 99
- Configure Plot view 100
- Setup field Purpose 101
- Setup field Purpose (Cont.) 102
- Graphing methods 103
- Restore default settings 104
- setting (explained above) 105
- Evaluating 106
- Custom tables 107
- NUMTYPE is set to 108
- Modifying Numeric Setup 109
- < scrolls the 109
- Adding a note to an app 110
- Creating an app 111
- I and use the 112
- E twice 112
- App functions and variables 113
- Function app 115
- Open the 116
- Define the 116
- Set up the 117
- Plot the 117
- Trace a 118
- Change the 118
- Function app 115 119
- Explore 120
- Numeric 120
- Num Step value) is 121
- Analyzing functions 122
- To find an 123
- Q1, and tap 123
- 120 Function app 124
- Function app 121 125
- The Function Variables 126
- To access Function 127
- Summary of FCN operations 128
- Advanced Graphing app 129
- 126 Advanced Graphing app 130
- Example 3 Example 4 130
- Example 5 Example 6 130
- 128 Advanced Graphing app 132
- Trace in Plot 133
- = and \ no longer jump from 134
- Advanced Graphing app 131 135
- Trace in 136
- Advanced Graphing app 133 137
- Plot Gallery 138
- Geometry 139
- Y Rng values 140
- Geometry 137 141
- Create a 142
- Add some 143
- P to return to 144
- M to return to Numeric view 144
- Plot view in detail 145
- E. Only by pressing E do 146
- Geometry 143 147
- Choose Color palette appears 148
- Select Object menu appears 148
- Choose Color 148
- Geometry 145 149
- Plot Setup view 150
- Result in Plot view 151
- Symbolic view in detail 152
- Geometry 149 153
- Numeric view in detail 154
- Geometry 151 155
- 152 Geometry 156
- Geometric objects 157
- 154 Geometry 158
- Geometry 155 159
- 156 Geometry 160
- Geometry 157 161
- 158 Geometry 162
- Geometry 159 163
- Plot, and 164
- Function 164
- Geometric transformations 165
- Reflection 166
- Dilation 166
- ∡ LKM in the 167
- 164 Geometry 168
- Symbolic view: Cmds menu 169
- 166 Geometry 170
- Geometry 167 171
- DrawSlp(a,b,m) 172
- Geometry 169 173
- 170 Geometry 174
- Geometry 171 175
- 172 Geometry 176
- Geometry 173 177
- 174 Geometry 178
- Geometry 175 179
- 176 Geometry 180
- Geometry 177 181
- Transform 182
- Geometry 179 183
- 180 Geometry 184
- Measure Plot 185
- Numeric view: Cmds menu 186
- Geometry 183 187
- 184 Geometry 188
- Geometry 185 189
- 186 Geometry 190
- Geometry 187 191
- 188 Geometry 192
- Other Geometry functions 193
- 190 Geometry 194
- LineHorz 195
- LineVert 195
- 192 Geometry 196
- Geometry 193 197
- 194 Geometry 198
- I and select 199
- S.PRICEs0.1E 200
- Column 201
- S.ANCOSTSE 202
- S.D3 w D5E 202
- S.D7 ≥ F1E 202
- Basic operations 203
- Cell references 204
- Cell naming 204
- Entering content 205
- is 59,049 206
- S.AAROOTAR3wAs 207
- External references 208
- Referencing variables 209
- 206 Spreadsheet 210
- Buttons and keys 211
- Formatting options 212
- Parameters 213
- Spreadsheet functions 214
- Statistics 1Var app 215
- 212 Statistics 1Var app 216
- Symbolic view: menu items 217
- 214 Statistics 1Var app 218
- > and < to 219
- + and w respectively 219
- Numeric view: menu items 220
- Edit a data 220
- Statistics 1Var app 217 221
- Computed statistics 222
- Plotting 223
- 220 Statistics 1Var app 224
- Exploring the graph 225
- Plot view: menu items 226
- Statistics 2Var app 227
- 224 Statistics 2Var app 228
- Statistics 2Var app 225 229
- 226 Statistics 2Var app 230
- Display the 231
- > until x = 6. If the 232
- Numeric view menu items 233
- SJ(Clear). Select the column 234
- Defining a regression model 235
- To define your 236
- Plotting statistical data 238
- Statistics 2Var app 235 239
- Plot setup 240
- Predicting values 241
- Troubleshooting a plot 242
- Inference app 243
- Symbolic view options 244
- Select the 245
- Plot the test 246
- Importing statistics 247
- Type and 248
- Hypothesis tests 249
- One-Sample Z-Test 250
- Two-Sample Z-Test 251
- One-Proportion Z-Test 252
- Two-Proportion Z-Test 253
- One-Sample T-Test 254
- Two-Sample T-Test 255
- Inputs The inputs are: 256
- Results The results are: 256
- Confidence intervals 257
- One-Proportion Z-Interval 258
- Two-Proportion Z-Interval 259
- One-Sample T-Interval 260
- Two-Sample T-Interval 260
- 258 Inference app 262
- Solve app 263
- One equation 264
- Solve app 261 265
- 262 Solve app 266
- Several equations 267
- Limitations 268
- Solution information 269
- Message Meaning (Continued) 270
- Linear Solver app 271
- Define and solve 272
- Menu items 273
- 270 Linear Solver app 274
- Parametric app 275
- Parametric app 273 277
- Explore the 278
- 276 Parametric app 280
- Polar app 281
- Set angle 282
- Sequence app 285
- 284 Sequence app 288
- Seq Plot and 289
- 286 Sequence app 290
- Finance app 291
- Q 300 move the cursor to 292
- Cash flow diagrams 293
- Time value of money (TVM) 294
- Finance app 291 295
- 292 Finance app 296
- Calculating amortizations 297
- 294 Finance app 298
- Finance app 295 299
- Triangle Solver app 300
- Specify the 301
- Choosing triangle types 302
- Special cases 303
- Triangle Solver app 299 304
- The Explorer apps 305
- 300 The Explorer apps 306
- The Explorer apps 301 307
- Quadratic Explorer app 308
- > or < to select 309
- Trig Explorer app 310
- The Explorer apps 305 311
- 306 The Explorer apps 312
- Functions and commands 313
- F). See “Math template” 314
- Setting the form 314
- Keyboard functions 315
- returns 1000 316
- Functions and commands 311 317
- 1– x 1 317
- 312 Functions and commands 318
- Math menu 319
- Arithmetic 320
- Functions and commands 315 321
- Trigonometry 322
- Hyperbolic 323
- Probability 323
- 318 Functions and commands 324
- Functions and commands 319 325
- Cumulative 326
- Functions and commands 323 329
- CAS menu 330
- Functions and commands 325 331
- Calculus 332
- Differential 333
- Integral 334
- 330 Functions and commands 336
- Functions and commands 331 337
- 332 Functions and commands 338
- Exp & Ln 339
- 338 Functions and commands 344
- Polynomial 345
- 340 Functions and commands 346
- Functions and commands 341 347
- 342 Functions and commands 348
- 344 Functions and commands 350
- 346 Functions and commands 352
- App menu 353
- Function app functions 354
- Solve app functions 355
- Spreadsheet app functions 355
- SUM([input]) 356
- AVERAGE([input]) 357
- "configuration"]) 357
- 352 Functions and commands 358
- Functions and commands 353 359
- 354 Functions and commands 360
- Functions and commands 355 361
- 356 Functions and commands 362
- HypZ1prop(x,n, 363
- ,,mode 363
- [”configuration”]) 363
- 358 Functions and commands 364
- HypT1mean( ,s,n, 365
- ,mode,[”configuration”]) 365
- "") 365
- 360 Functions and commands 366
- Functions and commands 361 367
- 362 Functions and commands 368
- Statistics 1Var app functions 369
- Frequency field for the H2 370
- Independent Column 370
- Statistics 2Var app functions 371
- Inference app functions 372
- Functions and commands 367 373
- 368 Functions and commands 374
- Functions and commands 369 375
- 370 Functions and commands 376
- Functions and commands 371 377
- Finance app functions 378
- Functions and commands 373 379
- Linear Solver app functions 380
- Triangle Solver app functions 380
- Functions and commands 375 381
- Linear Explorer functions 382
- Quadratic Explorer functions 383
- Common app functions 383
- Ctlg menu 384
- Functions and commands 379 385
- or Matrix1.*Matrix2 386
- [[3,8],[15,24]] 386
- or Matrix.^Integer 386
- Functions and commands 381 387
- 382 Functions and commands 388
- Functions and commands 383 389
- Functions and commands 393 399
- 396 Functions and commands 402
- Functions and commands 397 403
- 400 Functions and commands 406
- Functions and commands 401 407
- Functions and commands 403 409
- 408 Functions and commands 414
- Functions and commands 409 415
- Functions and commands 415 421
- Functions and commands 419 425
- Creating your own functions 427
- 422 Functions and commands 428
- Variables 429
- Working 430
- Home Settings screen (SH) 431
- Integer (for the 431
- More about 432
- Qualifying variables 433
- Home variables 434
- App variables 435
- Geometry app variables 436
- Spreadsheet app variables 437
- Solve app variables 437
- NumIndep 438
- Statistics 1Var app variables 439
- 434 Variables 440
- Statistics 2Var app variables 441
- 436 Variables 442
- Inference app variables 443
- 438 Variables 444
- Parametric app variables 445
- Polar app variables 446
- Finance app variables 446
- Linear Solver app variables 447
- Triangle Solver app variables 447
- Linear Explorer app variables 447
- Trig Explorer app variables 448
- Sequence app variables 448
- Units and constants 449
- Unit calculations 450
- Units and constants 445 451
- Unit tools 452
- Physical constants 453
- Value or 454
- List of constants 455
- 450 Units and constants 456
- Lists 451 457
- Button or Key Purpose 458
- The List Editor 459
- 454 Lists 460
- Deleting lists 461
- Lists in Home view 461
- 456 Lists 462
- List functions 463
- 458 Lists 464
- Lists 459 465
- 460 Lists 466
- Lists 461 467
- 462 Lists 468
- Matrices 469
- Creating and storing matrices 470
- Working with matrices 471
- 466 Matrices 472
- Matrices 467 473
- 468 Matrices 474
- Matrix arithmetic 475
- 470 Matrices 476
- Matrices 471 477
- 472 Matrices 478
- Matrices 473 479
- Matrix functions and commands 480
- Matrix functions 481
- (expression, elements) 482
- Matrices 477 483
- 478 Matrices 484
- Matrices 479 485
- Advanced 486
- Matrices 481 487
- 482 Matrices 488
- Factorize 489
- 484 Matrices 490
- Matrices 485 491
- Examples 492
- Matrices 487 493
- 488 Matrices 494
- Notes and Info 495
- The Note Editor 496
- Notes and Info 491 497
- Note Editor: buttons 498
- Keys Purpose 499
- Category Options (Continued) 501
- 496 Notes and Info 502
- Programming in HP PPL 503
- The Program Catalog 504
- Program 505
- Save creates a copy of 506
- Rename renames the 506
- Sort sorts the list of 506
- Delete deletes the 506
- Clear deletes all 506
- Creating a new program 507
- The Program Editor 508
- J to return to the 509
- 504 Programming in HP PPL 510
- Programming in HP PPL 505 511
- 506 Programming in HP PPL 512
- Debug a 513
- 508 Programming in HP PPL 514
- Programming in HP PPL 509 515
- 510 Programming in HP PPL 516
- To share a 517
- 512 Programming in HP PPL 518
- Programming in HP PPL 513 519
- ROLLMANY 520
- Programming in HP PPL 515 521
- 516 Programming in HP PPL 522
- Re-assigning 523
- Key Name 524
- App programs 526
- Program Name Equivalent 527
- Keystrokes 527
- Customizing 528
- I Select 529
- M and P 530
- S I to open the 530
- The DiceSimulation 530
- Programming in HP PPL 525 531
- The program 532
- DICESIMVARS 532
- Program commands 533
- Commands under the Tmplt menu 534
- Programming in HP PPL 529 535
- 530 Programming in HP PPL 536
- Programming in HP PPL 531 537
- 532 Programming in HP PPL 538
- Variable 539
- Commands under the Cmds menu 540
- String Result 541
- 536 Programming in HP PPL 542
- Programming in HP PPL 537 543
- Pixels and Cartesian 544
- Programming in HP PPL 539 545
- 540 Programming in HP PPL 546
- Programming in HP PPL 541 547
- 542 Programming in HP PPL 548
- Programming in HP PPL 543 549
- O to terminate 550
- Programming in HP PPL 545 551
- App Functions 552
- Programming in HP PPL 547 553
- 548 Programming in HP PPL 554
- Programming in HP PPL 549 555
- 550 Programming in HP PPL 556
- S J is pressed 557
- 552 Programming in HP PPL 558
- \ or = to view 559
- 554 Programming in HP PPL 560
- Programming in HP PPL 555 561
- Variables and Programs 562
- Programming in HP PPL 557 563
- Plot view variables 564
- min/max 566
- Symbolic view variables 568
- Programming in HP PPL 563 569
- Programming in HP PPL 565 571
- Y1;2*SIN(6*T) X1 571
- Numeric view variables 572
- Inference 574
- Programming in HP PPL 573 579
- LSystem 579
- 574 Programming in HP PPL 580
- AngleA 580
- AngleB 580
- AngleC 580
- Settings 581
- Symbolic 584
- Results 585
- 580 Programming in HP PPL 586
- Basic integer arithmetic 587
- The default base 588
- Changing the default base 589
- Mixed-base arithmetic 590
- Integer manipulation 591
- Base functions 592
- Appendix A 593
- Glossary 593
- 588 Glossary 594
- Glossary 589 595
- 590 Glossary 596
- Appendix B 597
- Troubleshooting 597
- Operating limits 598
- Status messages 598
- Troubleshooting 593 599
- 594 Troubleshooting 600
- Appendix C 601
- Chemical 605
- Substances 605
- Index 601 607
- 602 Index 608
- Index 603 609
- 604 Index 610
- Index 605 611
- 606 Index 612
- Index 607 613
- 608 Index 614
- Index 609 615
- 610 Index 616
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