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Strang G. — Linear Algebra and Its Applications
Strang G. — Linear Algebra and Its Applications



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Название: Linear Algebra and Its Applications

Автор: Strang G.

Аннотация:

Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Third Edition

Год издания: 1988

Количество страниц: 505

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Matrix, band      35 52 462
Matrix, checkerboard      129 253
Matrix, circulant      303
Matrix, coefficient      19
Matrix, cofactor      231
Matrix, companion      253
Matrix, consumption      269
Matrix, covariance      204
Matrix, cross-product      156 170
Matrix, defective      249 255 277 310
Matrix, diagonal      35 442
Matrix, diagonalizable      254 255 309 315 460
Matrix, difference      365
Matrix, echelon      72 77 82
Matrix, elementary      22 31 46
Matrix, exponential      276 459
Matrix, finite difference      53 222 365 386 467
Matrix, Fourier      183 188 299 303 321
Matrix, hermitian      294 300 309
Matrix, Hessenberg      205 373 377
Matrix, Hilbert      59 178
Matrix, identity      22
Matrix, ill-conditioned      56 363
Matrix, incidence      102 425 466
Matrix, indefinite      326 337
Matrix, inverse      32 42
Matrix, invertible      46
Matrix, Jordan      304 311 318 453
Matrix, lower triangular      32
Matrix, Markov      266 270 273 284
Matrix, mass      343 359
Matrix, multiplication      20 23 24 25 29 123 445
Matrix, nilpotent      321
Matrix, nondiagonalizable      249 255 277 310 453
Matrix, nonnegative      267 269
Matrix, nonsingular      13 14 38 46 71
Matrix, normal      297 311 315
Matrix, notation      21
Matrix, orthogonal      167 283 296 443
Matrix, payoff      435
Matrix, permutation      37 62 215
Matrix, positive      271
Matrix, positive definite      54 196 324 331 347
Matrix, projection      124 148 158 170 250 406
Matrix, rank one      98 261
Matrix, rectangular      21
Matrix, reflection      124 164 373
Matrix, rotation      30 122 257
Matrix, semidefinite      339
Matrix, similar      304 312
Matrix, singular      7 14 37 211
Matrix, skew-Hermitian      297 300 320
Matrix, skew-symmetric      28 436
Matrix, square root      261 334 337
Matrix, symmetric      48 290 309
Matrix, transition      267
Matrix, transpose      47 150 217
Matrix, triangular      27 216 308
Matrix, tridiagonal      53 377 462
Matrix, unitary      297 301 308
Max flow-min cut      425
Maximal      86
Maximin      350 434 437
Mean      165 171 465
Middle-aged      165
Millionaire      234
minimax      351 434 437 440 441
Minimax theorem      413
Minimum      322 325
Minimum principle      347
Minor      226
MIT      107
Mixed strategy      433
Modulus      291
Multiplication      20 21 24 29 123
Multiplicity      211 255
Multiplier      12 32 196 332 468
Natural boundary condition      359
Negative definite      325 338
NETLIB      193 464
Network      108 424
Neutrally stable      268 280
Newton’s law      284 343
Newton’s method      372
Nilpotent      321
Node      102
Nondiagonalizable      310 460
NonNegative      267 269 419
Nonsingular      13 14 38 46 71
Nontrivial      80
Norm      362 366 368 369
Normal equation      156 446
Normal matrix      297 311 315 317
Normal mode      249 280
Nullity      92 199 201
NullSpace      68 74 92 136 246
Objective function      390
Odd permutation      237 240 468
Ohm’s Law      109
Operation      15 40 45 55
Optimality      401 414 415 447
Orange      108
Orthogonal      134 177 300
Orthogonal complement      138
Orthogonal eigenvectors      295 315
Orthogonal matrix      167 283 296 443
Orthogonal subspace      135 138 301
Orthogonalization      172 179 196
Orthonormal      135 166 169 174 311
Oscillation      244 284 322 343
Overdetermined      145
Overrelaxation      381 382
PA=LU      38 73 462
Pancake      144
parallel      4 16 76
Parallelepiped      212 234
Parallelogram      4 235
Parentheses      23 26
Partial pivoting      58 59 465
Particular solution      76
Payoff      435
PC      15 17
Peanut butter      392
Permutation      129 224 237
Permutation matrix      37 62 215
Perpendicular      134 155
Perron      271
Perturbation      57
Phase I and II      398 410
Piecewise polynomial      356
Pivot      12 13 36 72 212 236 332 445
Plane      2 5
Plane rotation      316 377
Poker      439
Polar coordinates      212 292
Polar decomposition      445
Polynomial      98
Polynomial time      407
Positive definite      54 196 324 331 347 445
Positive matrix      271
Potential      103
Power method      370 379
Powers of matrices      258 314
Preconditioner      381
Premultiplication      26
Pricing out      401
Primal      412
Principal axis      296 336 446
Principal submatrix      339
Prisoner      185 439
PRODUCT      123 201 217 240 259
Product form      404
Product of pivots      222
Professor      207
Projection      117 123 144 164 250 306 406
Projection matrix      148 158 170
Pseudoinverse      97 141 154 448 449
Pure exponential      245 248
Pure power      264
Pythagoras      133 169 180 448
QR factorization      174 176 376
QR method      342 376
Quadratic      246 323 348
quantum mechanics      260
Random number      465 466 471
RANGE      92
Rank      76 80 100 129 201 202 445
Rank one      98 148 261
Rayleigh - Ritz      356 360
Rayleigh quotient      348 353 358 372
Reduced cost      401 418
Reduced factorization      195 197 206
Reflection      116 124 164 168 180 373
Regression      145
Relativity      5
Repeated eigenvalues      256 310 312 454
Rescaling      59 407 408
Revised simplex      404
Right-handed      168 234
Right-inverse      42 90 96 452
Roof function      357
Roots of unity      184 186 299
Rotation      116 167 257 446
Rotation matrix      30 122
Roundoff error      37 56 365 445
Routh      282
Row at a time      20 25
Row exchange      24 36 37 215 225
Row picture      7 21
Row rank = column rank      93
Row space      90 91 136 141 302 448
Row-reduced echelon form      77
Saddle point      326 433 437
scalar      6 134
Schur complement      239
Schur’s lemma      307
Schwarz inequality      145 147 151 177 260 338
Second-order equation      284
Semicircle law      466
Semidefinite      325 339 445
Sensitivity      364 417
Separating hyperplane      419 420
Shadow price      413 417
shearing      125 235
Shift      371 376
Signs of eigenvalues      339 342
Similar      304 306 312 315 454 457
Simplex method      391 395 404 464
Simultaneous      344 352
singular      7 14 37 216
Singular value      368 369
Singular value decomposition      141 195 375 443 450
Skew-Hermitian      297 300 320
Skew-symmetric      50 220 283 288 436
Slack variable      392 397
solvable      66 100 139 418
SOR      383 467
Space      63 69
span      83
Spanning tree      106 429 466
sparse      52 355 360 465
Spectral radius      381
Spectral theorem      296 309
Splitting      380
Square root      261 334 337
Stable      244 268 280 309 338 444
Standard basis      166
Statistics      156 165 204 466
Steady state      18 52 267
Stiffness matrix      357
Stopping test      401
Straight line      161 164 172 180
String of eigenvectors      454
SubMatrix      202 236 330 339
subspace      64 69
Subspace intersection      198
Subspace, fundamental      90 95 136 302
Subspace, orthogonal      135
SUM      198
Sum of squares      153 325 328 332
Summation      21 29 134
Sunflower      263
Superposition      248
Sylvester      314
Symmetric matrix      48 290 309 327
table      300 315
Tableau      400 403
Taylor series      327
Tensor notation      21
tetrahedron      151
Thorp      439
Trace      151 251 252 261 281
Transformation      116
Transition matrix      267
Transportation problem      394 430
TRANSPOSE      47 150 217 294
TREE      105
Triangle inequality      151 369
Triangular factorization      34 36 73
Triangular matrix      27 34 216 308
Tridiagonal      53 377 462
Trivial      80 263
Tukey      190
Uncertainty principle      260
Underdetermined      71
Uniqueness      96
Unit circle      184 292
Unit vector      166
Unitary matrix      297 301 308
Unstable      268 280 57
Upper triangular      31
Value      434
Vandermonde      98 220 242
Variance      165 204
Vector      5
Vector space      63 69 197
Voltage law      104
Volume      212 234
von Neumann      56 271 437
Wave equation      286
Weak duality      413
Weighted      203 409
Wilkinson      56 367
wronskian      277
X-ray      20
Young      384
Zero eigenvalue      250
Zero in pivot position      13 37 237
Zero submatrix      207 229
Zero-sum game      435
Zurich      16
1 2
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