Topics in Matrix AnalysisCambridge University Press, 24 juin 1994 - 607 pages Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics with important applications and of special mathematical interest in matrix theory not included in the previous text. These topics include the field of values, stable matrices and inertia, singular values, matrix equations and Kronecker products, Hadamard products, and matrices and functions. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. The book should be welcomed by graduate students and researchers in a variety of mathematical fields both as an advanced text and as a modern reference work. |
Table des matières
II | 1 |
III | 5 |
IV | 8 |
V | 17 |
VI | 28 |
VII | 30 |
VIII | 48 |
IX | 65 |
XXVII | 241 |
XXVIII | 242 |
XXIX | 254 |
XXX | 268 |
XXXI | 288 |
XXXII | 298 |
XXXIII | 304 |
XXXIV | 308 |
X | 77 |
XI | 89 |
XII | 91 |
XIII | 95 |
XIV | 101 |
XV | 102 |
XVI | 112 |
XVII | 134 |
XVIII | 144 |
XIX | 163 |
XX | 170 |
XXI | 195 |
XXII | 203 |
XXIII | 217 |
XXIV | 223 |
XXV | 231 |
XXVI | 239 |
XXXV | 312 |
XXXVI | 322 |
XXXVII | 332 |
XXXIX | 349 |
XL | 356 |
XLII | 382 |
XLIII | 383 |
XLIV | 407 |
XLV | 449 |
XLVI | 459 |
XLVII | 490 |
XLVIII | 520 |
XLIX | 561 |
L | 584 |
LI | 590 |
595 | |
Expressions et termes fréquents
A E M₂ A₁ assertion B₁ B₂ coefficients column commutes complex consider convex matrix function Corollary decreasingly ordered defined denote diagonalizable diagonally dominant doubly stochastic eigenvalues eigenvector equivalent example Exercise field of values formula function f given matrix Hadamard product half-plane Hermitian matrices identity inequalities Jordan blocks Jordan canonical form Kronecker product Lemma Let A E M-matrix M₁ M₂ M₂ be given M₂(R main diagonal entries Math matrix equations matrix norm minimal polynomial monotone matrix function multiplicities nonnegative nonnegative matrix nonsingular nonzero normal normal matrix nullspace orthogonal permutation matrix positive semidefinite positive stable primary matrix function principal submatrix Problem rank result satisfies scalar Section singular value decomposition solution spectral norm square root suppose symmetric t₁ tion unitarily invariant norm unitarily similar unitary matrix upper triangular vector Verify weak majorization zero