The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

conditions and an accurate semidefinite programming solver," The Journal of the SDPA family for solving large-scale SDPs," in Handbook on Semidefinite. Semidefinite Programming, Combinatorial. Optimization and Primal semidefinite programming problem Handbook of Semidefinite Programming. Kluwer. Solving Euclidean distance matrix completion problems via semidefinite programming. AY Alfakih, A Khandani, H Wolkowicz. Computational optimization.

/pdf/handbook-of-semidefinite-programming-1hywp52iad.pdf

Handbook of Semidefinite Programming

Concrete mathematics, a foundation for computer science, by Ronald L. Graham, Donald E. Knuth and Oren Patashnik. Pp 625. £24·95. 1989. ISBN 0-201-14236-8 (Addison-Wesley)

"Matrix Mathematics" is a reference work for users of matrices in all branches of engineering, science, and applied mathematics. This book brings together a vast body of results on matrix theory for easy reference and immediate application. Each chapter begins with the development of relevant background theory followed by a large collection of specialized results. Hundreds of identities, inequalities, and matrix facts are stated rigorously and clearly with cross references, citations to the literature, and illuminating remarks. Twelve chapters cover all of the major topics in matrix theory: preliminaries; basic matrix properties; matrix classes and transformations; matrix polynomials and rational transfer functions; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; norms; functions of matrices and their derivatives; the matrix exponential and stability theory; and linear systems and control theory. A detailed list of symbols, a summary of notation and conventions, an extensive bibliography with author index, and an extensive index are provided for ease of use. The book will be useful for students at both the undergraduate and graduate levels, as well as for researchers and practitioners in all branches of engineering, science, and applied mathematics.

/pdf/matrix-mathematics-theory-facts-and-formulas-with-8swhnd659u.pdf

Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory

A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized. A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include: * Complex matrices * A wide range of special matrices and their properties * Special products and operators, such as the Kronecker product * Partitioned and patterned matrices * Matrix analysis and approximation * Matrix optimization * Majorization * Random vectors and matrices * Inequalities, such as probabilistic inequalities Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers.

A matrix handbook for statisticians

Let A and B be complex matrices of same dimension. Given their eigen- values and singular values, we survey and further develop simple inequalities for eigenvalues and singular values of A + B, AB ,a ndA ◦ B.H ere◦ denotes the Hadamard product. As corollaries, we find inequalities for additive and multi- plicative spreads of these matrices.

Jorma K. Merikoski

Papers

Inequalities for spreads of matrix sums and products.

Characterizations and lower bounds for the spread of a normal matrix

A best upper bound for the 2-norm condition number of a matrix

Bounds for Eigenvalues Using the Trace and Determinant

On the trace and the sum of elements of a matrix