Page 3 - Matrix Analysis & Applied Linear Algebra
P. 3
vi Contents
4.5 More about Rank . .............. 210
4.6 Classical Least Squares ............ 223
4.7 Linear Transformations ............ 238
4.8 Change of Basis and Similarity ......... 251
4.9 Invariant Subspaces .............. 259
5. Norms, Inner Products, and Orthogonality . . 269
5.1 Vector Norms . . .............. 269
5.2 Matrix Norms . . .............. 279
5.3 Inner-Product Spaces ............. 286
5.4 Orthogonal Vectors .............. 294
5.5 Gram–Schmidt Procedure ........... 307
5.6 Unitaryand Orthogonal Matrices ........ 320
5.7 Orthogonal Reduction ............. 341
5.8 Discrete Fourier Transform ........... 356
5.9 ComplementarySubspaces ........... 383
5.10 Range-Nullspace Decomposition ........ 394
5.11 Orthogonal Decomposition ........... 403
5.12 Singular Value Decomposition ......... 411
5.13 Orthogonal Projection ............. 429
5.14 WhyLeast Squares? .............. 446
5.15 Angles between Subspaces ........... 450
6. Determinants ............... 459
6.1 Determinants . . . .............. 459
6.2 Additional Properties of Determinants ...... 475
7. Eigenvalues and Eigenvectors ........ 489
7.1 ElementaryProperties of Eigensystems ..... 489
7.2 Diagonalization bySimilarityTransformations . . 505
7.3 Functions of Diagonalizable Matrices ...... 525
7.4 Systems of Differential Equations ........ 541
7.5 Normal Matrices . .............. 547
7.6 Positive Definite Matrices ........... 558
7.7 Nilpotent Matrices and Jordan Structure .... 574
7.8 Jordan Form . . . .............. 587
7.9 Functions of Nondiagonalizable Matrices ..... 599
