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Marvin Marcus Henryk A Survey of Matrix Theory and Matrix Inequali (Paperback)

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Objectstaat
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Book Title
A Survey of Matrix Theory and Matrix Inequalities
Publication Name
Survey of Matrix Theory and Matrix Inequalities
Title
A Survey of Matrix Theory and Matrix Inequalities
Author
Marvin Marcus, Henryk Minc
Format
Trade Paperback
ISBN-10
048667102X
EAN
9780486671024
ISBN
9780486671024
Publisher
Dover Publications, Incorporated
Genre
Science Nature & Math
Release Year
2010
Release Date
16/09/2010
Language
English
Country/Region of Manufacture
US
Item Height
0.4in
Item Length
8.5in
Item Width
5.4in
Item Weight
7.9 Oz
Series
Dover Books on Mathematics Ser.
Publication Year
2010
Type
Textbook
Number of Pages
180 Pages

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Product Information

Concise, masterly survey of a substantial part of modern matrix theory introduces broad range of ideas involving both matrix theory and matrix inequalities. Also, convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, more. Undergraduate-level. 1969 edition. Bibliography.

Product Identifiers

Publisher
Dover Publications, Incorporated
ISBN-10
048667102x
ISBN-13
9780486671024
eBay Product ID (ePID)
28038313060

Product Key Features

Author
Marvin Marcus, Henryk Minc
Publication Name
Survey of Matrix Theory and Matrix Inequalities
Format
Trade Paperback
Language
English
Publication Year
2010
Series
Dover Books on Mathematics Ser.
Type
Textbook
Number of Pages
180 Pages

Dimensions

Item Length
8.5in
Item Height
0.4in
Item Width
5.4in
Item Weight
7.9 Oz

Additional Product Features

Lc Classification Number
Qa188.M36
Edition Description
Reprint,New Edition
Table of Content
I. SURVEY OF MATRIX THEORY 1. INTRODUCTORY CONCEPTS Matrices and vectors. Matrix operations. Inverse. Matrix and vector operations. Examples. Transpose. Direct sum and block multiplication. Examples. Kronecker product. Example. 2. NUMBERS ASSOCIATED WITH MATRICES Notation. Submatrices. Permutations. Determinants. The quadratic relations among subdeterminants. Examples. Compound matrices. Symmetric functions; trace. Permanents. Example. Properties of permanents. Induced matrices. Characteristic polynomial. Examples. Characteristic roots. Examples. Rank. Linear combinations. Example. Linear dependence; dimension. Example. 3. LINEAR EQUATIONS AND CANONICAL FORMS Introduction and notation. Elementary operations. Example. Elementary matrices. Example. Hermite normal form. Example. Use of the Hermite normal form in solving Ax = b. Example. Elementary column operations and matrices. Examples. Characteristic vectors. Examples. Conventions for polynomial and integral matrices. Determinantal divisors. Examples. Equivalence. Example. Invariant factors. Elementary divisors. Examples. Smith normal form. Example. Similarity. Examples. Elementary divisors and similarity. Example. Minimal polynomial. Companion matrix. Examples. Irreducibility. Similarity to a diagonal matrix. Examples. 4. "SPECIAL CLASSES OF MATRICES, COMMUTATIVITY" Bilinear functional. Examples. Inner product. Example. Orthogonality. Example. Normal matrices. Examples. Circulant. Unitary similarity. Example. Positive definite matrices. Example. Functions of normal matrices. Examples. Exponential of a matrix. Functions of an arbitrary matrix. Example. Representation of a matrix as a function of other matrices. Examples. Simultaneous reduction of commuting matrices. Commutativity. Example. Quasi-commutativity. Example. Property L. Examples. Miscellaneous results on commutativity. 5. CONGRUENCE Definitions. Triple diagonal form. Congruence and elementary operations. Example. Relationship to quadratic forms. Example. Congruence properties. Hermitian congruence. Example. Triangular product representation. Example. Conjunctive reduction of skew-hermitian matrices. Conjunctive reduction of two hermitian matrices.II. CONVEXITY AND MATRICES 1. CONVEX SETS Definitions. Examples. Intersection property. Examples. Convex polyhedrons. Example. Birkhoff theorem. Simplex. Examples. Dimension. Example. Linear functionals. Example. 2. CONVEX FUNCTIONS Definitions. Examples. Properties of convex functions. Examples. 3. CLASSICAL INEQUALITIES Power means. Symmetric functions. Hölder inequality. Minkowski inequality. Other inequalities. Example. 4. CONVEX FUNCTIONS AND MATRIX INEQUALITIES Convex functions of matrices. Inequalities of H. Weyl. Kantorovich inequality. More inequalities. Hadamard product. 5. NONNEGATIVE MATRICES Introduction. Indecomposable matrices. Examples. Fully indecomposable matrices. Perron-Frobenius theorem. Example. Nonnegative matrices. Examples. Primitive matrices. Example. Doubly stochastic matrices. Examples. Stochastic matrices.III. LOCALIZATION OF CHARACTERISTIC ROOTS 1. BOUNDS FOR CHARACTERISTIC ROOTS Introduction. Bendixson's theorems. Hirsch's theorems. Schur's inequality (1909). Browne's theorem. Perron's theorem. Schneider's theorem. 2. REGIONS CONTAINING CHARACTERISTIC ROOTS OF A GENERAL MATRIX. Lévy-Desplanques theorem. Gersgorin discs. &
Copyright Date
1992
Target Audience
College Audience
Topic
Matrices
Lccn
91-039704
Dewey Decimal
512.9/434
Dewey Edition
20
Genre
Mathematics

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