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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
$?\neq NP$      405
$A=LDL^{T}      $48 195 332
$A=MJM^{-1}$      312 453
$A=Q\bigwedge Q^{T}$      296 309 334 443
$A=Q_{1}\sum Q_{2}^{T}$      375 443
$A=SAS^{-1}$      254
$A=uv^{T}$      99
$A=\underline{L}\underline{U}$      197 206 452
$AA^{O}$      50 442
$A^{T}A$      50 156 210 442 446
$A^{T}CA$      111
$C^{n}$      258 290 300
$LDL^{T}$ factorization      48 332
$R^{n}$      63 86
$S^{-1}AS$      125 254
$\underline{L}\underline{U}$ factorization      197 206
A=LDU      36 236
A=LPU      38 41
A=LU      32 33 40 73 468
A=QR      174 176 374
A=QS      445
Absolute value      291
Addition of vectors      6
Adjugate matrix      232
Almost periodic      286
alternative      142 418 420
Area      235 239
Arithmetic mean      147 150
Associative      25 29
Associative law      23 126
Average      405 465
axes      132 296 335
Back-substitution      12 15 468
Band matrix      35 52 55 462
Bandwidth      55
Basic variable      73 76 398
Basis      84 125 305 316 443
Bidiagonal      54
Bit-reversed      193
Block      371
Block elimination      239
Block multiplication      30 236
Block of zeros      207 229 428
Bomb      284
Boolean algebra      215
Boundary condition      52 59
Breakdown      13
Bridge      205 248
Buniakowsky      148
Butterfly      193
California      18 266 370
Capacity      424
Cauchy      148
Cayley-Hamilton      317 460
CD=-DC      29 221 242 315
Chain of matrices      241 345
Change of basis      125 305 316
Change of variables      304 341
Characteristic equation      246 317
Characteristic polynomial      246
Checkerboard      129 253
Chemist      151
Chess      438 441
cholesky      195 334 462
Circulant      303
Cofactor      226
Cofactor matrix      231
Column at a time      20 43 463
Column picture      7 21
Column space      66 93 136 141
Column vector      5
Columns times rows      29 206 445
Combination of columns      21 25 66
Combination of rows      22 25
Commutative      23 26
Commute      27 29 259
Companion matrix      253
Complement      138
Complementary slackness      415
Complete the square      325 329 352
Complex conjugate      291 294 300
Complex number      183 257 290
Complex plane      184 291
composition      123
Compound interest      262
Computer      2 14 28 465
Condition number      362 364 367 368 463 466
Cone      419
Congruence      341
conjugate      291 301
Conjugate gradient      385 409
Conjugate transpose      293
Constraint      392
Consumption matrix      269
Convolution      183 303
Cooley      190
Coordinate      5 166
Corner      391 396
Cosine      145 148 177
Cost      14
Cost function      390
Covariance matrix      204
Cramer’s Rule      1 233 239
Cray      17 28
Cross-product matrix      156 170
Cross—product      288
Crout      36
CT scanner      209
Current law      104
Curse      385
Cut      425 428
Cycling      400
Dantzig      395 438
Defective      249 255 277 310
Degeneracy      399
Degree of freedom      74 85 302
Dependent      80 82
Descartes      5
Determinant      44 211 216 251 427
Determinant, formula      222 224 226
Diagonal matrix      36 254 442
Diagonalizable      255 259 309 460
Diagonalization      254 256
Diagonally dominant      387
Diet problem      392 412
Difference equation      53 262 265 274
Differential equation      52 244 277 314 458
Differentiation      118 120 316
Diffusion      278 287
DIMENSION      74 85 86 95 200
Direct sum      206
Directed graph      102
Discrete      53
Discrete transform      183
Distance      209
Distinct eigenvalues      255
Distributive      26
Dual      392 412
Duality      413 416 427
Dynamic programming      430
Echelon      72
Echelon matrix      77 82
Economics      269
EDGE      102 396
Effective rank      445
Eigenfunction      280
Eigenvalue      245 249 258 331 370
Eigenvalue matrix      254
Eigenvector      245 247 295 315
Eigenvector matrix      254 443
Einstein      21
EISPACK      461
Elementary matrix      22 31 46
Elimination      1 13 31 43 72 77 236
ellipse      296
Ellipsoid      177 334 350
Energy      347
Entering variable      398 401
Equality constraint      397
Equilibrium      112 348
Error      153
Error vector      155 158
Euler’s formula      106
Even permutation      237 468
Existence      96
Experiment      465
Exponential      275 283 314 459
Factorization      2 32 192 468
Fast Fourier Transform      183 189 299 303 385 464
Feasible set      390
fibonacci      228 263 272 319
Filippov      312 455
Finite difference      53 280 355
Finite difference matrix      222 365 386
Finite element method      355
First-order      244 278
Fitting data      159
Five-point matrix      385 467
Football      106 335 441
Formula for pivots      235
FORTRAN      28 463 468
Forward elimination      13 15 31
Four fundamental subspaces      90 443
Fourier matrix      183 188 299 303 321
Fourier series      168 176
Fredholm      142 418
Free variable      73 76 398
frequency      286
Frobenius      271
Front wall      136
Function space      64 177
Fundamental subspace      90 136 302 443
Fundamental theorem      95 104 138
Gale      420 438
Galerkin      360
Galois      251
Game      433
Gauss-Jordan      43 46 77
Gauss-Seidel      381 467
Gaussian elimination      1 12 38 236
Geiger counter      162
General solution      73 76 277 459
Generalized eigenvalue problem      289 343 345 352 359
Generalized eigenvector      277 454
Geodesy      145
Gershgorin      386
givens      342
Golub      385
Gram-Schmidt      166 172 176 181 196 341 375
Graph      102 106 466
Greedy algorithm      430
Grounded      110
Group      62
Halfspace      389
Hall’s condition      428 431
Harvard      107
Heat equation      280
Heisenberg      260
Hermitian matrix      294 300 309
Hertz      175
Hessenberg      205 373 377
hessian      327
Hilbert matrix      59 178
Hilbert space      177
Hogben      234
Homogeneous      68 74
Homotopy      341
Householder      180 373 378
Hurwitz      282
IBM      16
Identity matrix      22
Ill-conditioned      56 363
Image processing      444
Imaginary number      183 257
Incidence matrix      102 425 466
Incomplete LU      386
Inconsistent      8 71 153
indefinite      326 337
Independence      80 82 256
Inequality      389 418
Infinite-dimensional      64 177
Infinity of solutions      8
Inhomogeneous      74
Inner product      20 28 134 177 204 293
Input-output      269
Integration      118
Interest      262
Intersection      198
Intertwining      350
Invariant      341
Inverse      32 42
Inverse of product      43
Inverse of transpose      47
Inverse power method      371
Inverse, formula      231
Invertible      42 46
Isomorphism      200
iterative      361 381 387
Jacobi method      372 381 467
Jacobian determinant      212 239
Jordan form      304 311 318 453
Karmarkar      388 391 405
Kernel      92
Khachian      405
Kirchhoff      104 109 139 424
KRYLOV      378
Kuhn-Tucker      415 438
Labeling algorithm      426
Lagrange multiplier      415
Lanczos      378
Laplace      385 467
Las Vegas      439
Law of inertia      339 341 345 353
LDU factorization      36 236
Least squares      108 154 156 204 353 446 450 462
Leaving variable      398 401
Left nullspace      90 94 103 136
Left-inverse      42 90 96 100 121 170 452
legendre      179
Length      133 168 177 204 290 293
Leontief      269
linear combination      7
Linear independence      80 82 256
Linear programming      388 392 464
Linear transformation      117 120 305
LINPACK      461
Loop      103 106 429
Lower triangular      27 32
LU factorization      32 40 73
Lyapunov      282 338
M-orthogonal      344 346
MacSimplex      465
Markov matrix      266 270 273 284
Marriage problem      426
Mass matrix      289 343 359
Matching      426 428
MATLAB      464
Matrix      19
Matrix, 0-1      60 427 465
Matrix, adjacency      466
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