Introduction to Matrix Analysis: Second Edition
Long considered to be a classic in its field, this was the first book in English to include three basic fields of the analysis of matrices - symmetric matrices and quadratic forms, matrices and differential equations, and positive matrices and their use in probability theory and mathematical economics. Written in lucid, concise terms, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods. Originally published in 1970, this book replaces the first edition previously published by SIAM in the Classics series. Here you will find a basic guide to operations with matrices and the theory of symmetric matrices, plus an understanding of general square matrices, origins of Markov matrices and non-negative matrices in general, minimum-maximum characterization of characteristic roots, Kronecker products, functions of matrices, and much more. These ideas and methods will serve as powerful analytical tools.
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algebraic analysis analytic Appl Bellman Cayley–Hamilton theorem Chap characteristic roots characteristic values characteristic vector associated coefficients complex components computational Consider convergence defined denote derive determinantal diagonal form discussion distinct characteristic roots Duke Math Dynamic Programming elements exists foregoing functional equation given Hence Hermitian Matrices inequality integral Invariant Imbedding inverse Kronecker Kronecker product Ky Fan Laplace transform linear equations linear systems Markoff matrix mathematical matrix theory method minimizing minimum MISCELLANEOUS EXERCISES multiple necessary and sufficient non-negative definite nonsingular notation obtain orthogonal matrix polynomial positive definite positive matrix probability vector problem of determining Proc proof quadratic form quantities real symmetric recurrence relation representation result satisfying scalar sequence Show stability stochastic sufficient condition symmetric matrices Taussky techniques Theorem tion unique unitary unitary matrix variables write zero