Graham A. Nonnegative Matrices and Applicable Topics in Linear Algebra 2019 torrent

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Nonnegative matrices is an increasingly important subject in economics, control theory, numerical analysis, Markov chains, and other areas. This concise treatment is directed toward undergraduates who lack specialized knowledge at the postgraduate level of mathematics and related fields, such as mathematical economics and operations research. An Introductory Survey encompasses some aspects of matrix theory and its applications and other relevant topics in linear algebra, including certain facets of graph theory. Subsequent chapters cover various points of the theory of normal matrices, comprising unitary and Hermitian matrices, and the properties of positive definite matrices. An exploration of the main topic, nonnegative matrices, is followed by a discussion of M-matrices. The final chapter examines stochastic, genetic, and economic models. The important concepts are illustrated by simple worked examples. Problems appear at the conclusion of most chapters, with solutions at the end of the book.
Preface
Examples of Notation Used
Introductory Survey
Introduction
Notation
Submatrices and Minors
Expressing a Singular Matrix as a Product
Determinants
The Derivative of a Determinant
The Characteristic Equation
The Adjoint of the Characteristic Matrix
Spectral Decomposition
Inner Product and Norms
The Trace Function
Permutation Matrices and Irreducible Matrices
Some Aspects of the Theory of Graphs
Matrix Convergence
Some Matrix Types
Introduction
Unitary Matrices
Hermitian Matrices
Normal Matrices
Problems
Positive Definite Matrices
Introduction
Quadratic Forms
Reductions to a Canonical Form
A Geometrical Application
Problems
Positive Definite Matrices
Nonnegative Matrices
Introduction
Terminology and Notation
The Perron–Frobenius Theorem for a Positive Matrix
Irreducible Matrices
Cyclic Matrices
Reducible Matrices
Problems
M-Matrices
Introduction
Non-singular M-Matrices
Regular Splitting and Solving Simultaneous Equations
Problems
Finite Markov Chains and Stochastic Matrices
Some Applications of Nonnegative Matrices
Introduction
Some Genetic Models
Some Economic Models
Some Markov Chain Models
Appendix
Solutions to Problems
References
Index