线性代数及其应用(第三版.英文版)

.2.6 the leontief input-output model 152
2.7 applications to computer graphics 158
2.8 subspaces of rn 167
2.9 dimension and rank 176
supplementary exercises 183
chpater 3 determinants 185
introductory example: determinants in analytic geometry 185
3.1 introduction to determinants 186
3.2 properties of determinants 192
3.3 cramer's rule, volume, and linear transformations 201
supplementary exercises 211
chpater 4 vector spaces 215
introductor.v example: space flight and control systems 215
4.1 vector spaces' and subspaces 216
4.2 null spaces, column spaces, and linear transformations 226
4.3 linearly independent sets; bases 237
4.4 coordinate systems 246
4.5 the dimension of a vector space 256
4.6 rank 262
4.7 change of basis 271
4.8 applications to difference equations 277
4.9 applications to markov chains 288
supplementary exercises 299
chpater 5 eigenvalues and eigenvectors 301
introductory example: dynamical systems and spotted owls 301
5.1 eigenvectors and eigenvalues 302
5.2 the characteristic equation 310
5.3 diagonalization 319
5.4 eigenvectors and linear transformations 327
5.5 complex eigenvalues 335
5.6 discrete dynamical systems 342
5.7 applications to differential equations 353
5.8 iterative estimates for eigenvalues 363
supplementary exercises 370
chpater 6 orthogonality and least squares 373
introductory example: readjusting the north american datum 373
6.1 inner product, length, and orthogonality 375
6.2 orthogonal sets 384
6.3 orthogonal projections 394
6.4 the gram-schmidt process 402
6.5 least-squares problems 409
6.6 applications to linear models 419
6.7 inner product spaces 427
6.8 applications of inner product spaces 436
supplementary exercises 444
chpater 7 symmetric matrices and quadratic forms 447
introductory example: multichannel image processing
7.1 diagonalization of symmetric matrices 449
7.2 quadratic forms 455
7.3 constrained optimization 463
7.4 the singular value decomposition 471
7.5 applications to image processing and statistics 482
supplementary exercises 491
appendixes
a uniqueness of the reduced echelon form a1
b complex numbers a3
glossary a9
answers to odd-numbered exercises a19
index i1