Matrix AnalysisCambridge University Press, 22 okt 2012 Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This second edition of this acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme and demonstrates their importance in a variety of applications. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices, and much more. |
Inhoudsopgave
| 1 | |
Eigenvalues Eigenvectors and Similarity | 43 |
Unitary Similarity and Unitary Equivalence | 83 |
Canonical Forms for Similarity and Triangular Factorizations | 163 |
Hermitian Matrices Symmetric Matrices and Congruences | 225 |
Norms for Vectors and Matrices | 313 |
Location and Perturbation of Eigenvalues | 387 |
Veelvoorkomende woorden en zinsdelen
algebraic Apply assertion associated assume basis block bound characteristic column commutes complex conclude condition congruence Consider contains continuous Conversely convex Corollary decomposition defined determined diagonalizable direct distinct e Mn eigenvalues eigenvector ensures equality equivalent example Exercise Explain factorization function given gives hence Hermitian Hermitian matrix identity inequality invariant irreducible Jordan canonical form least Lemma linear main diagonal entries matrix norm multiplicity nonnegative nonsingular nonzero normal observation obtain orthogonal matrix orthonormal pair partitioned permutation polynomial positive definite positive semidefinite preceding principal problem Proof prove Provide rank real orthogonal respectively result satisfies scalar Show similar simultaneously singular values spectral square Suppose symmetric symmetric matrix theorem Type unique unit unitary upper triangular vector vector space Verify zero