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Nonnegative Matrices and Applicable Topics in Linear Algebra Dover Books on Mathematics 1st Edition by Alexander Graham ISBN 9780486838076 0486838072

Name: Nonnegative Matrices and Applicable Topics in Linear Algebra Dover Books on Mathematics 1st Edition by Alexander Graham ISBN 9780486838076 0486838072
SKU: EB-51158830
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Nonnegative Matrices and Applicable Topics in Linear Algebra Dover Books on Mathematics Alexander Graham Digital Instant Download

Author(s): Alexander Graham

ISBN(s): 9780486838076, 0486838072

Edition: Illustrated

File Details: DJVU, 1.54 MB

Year: 2019

Language: English

SKU: EB-51158830 Category: Uncategorized Tag: Alexander Graham

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Nonnegative Matrices and Applicable Topics in Linear Algebra Dover Books on Mathematics 1st Edition by Alexander Graham – Ebook PDF Instant Download/Delivery: 9780486838076 ,0486838072
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ISBN 10: 0486838072
ISBN 13: 9780486838076
Author: Alexander Graham

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.

Nonnegative Matrices and Applicable Topics in Linear Algebra Dover Books on Mathematics 1st Edition Table of contents:

Chapter 1. Introductory Survey

1.1 Introduction

1.2 Notation

1.3 Submatrices and Minors

1.4 Expressing a Singular Matrix as a Product

1.5 Determinants

1.6 The Derivative of a Determinant

1.7 The Characteristic Equation

1.8 The Adjoint of the Characteristic Matrix

1.9 Spectral Decomposition

1.10 Inner Product and Norms

1.11 The Trace Function

1.12 Permutation Matrices and Irreducible Matrices

1.13 Some Aspects of the Theory of Graphs

1.14 Matrix Convergence

Chapter 2. Some Matrix Types

2.1 Introduction

2.2 Unitary Matrices

2.3 Hermitian Matrices

2.4 Normal Matrices

Problems

Chapter 3. Positive Definite Matrices

3.1 Introduction

3.2 Quadratic Forms

3.3 Reductions to a Canonical Form

3.4 A Geometrical Application

Problems

3.5 Positive Definite Matrices

Chapter 4. Nonnegative Matrices

4.1 Introduction

4.2 Terminology and Notation

4.3 The Perron–Frobenius Theorem for a Positive Matrix

4.4 Irreducible Matrices

4.5 Cyclic Matrices

4.6 Reducible Matrices

Problems

Chapter 5. M-Matrices

5.1 Introduction

5.2 Non-singular M-Matrices

5.3 Regular Splitting and Solving Simultaneous Equations

Problems

Chapter 6. Finite Markov Chains and Stochastic Matrices

Chapter 7. Some Applications of Nonnegative Matrices

7.1 Introduction

7.2 Some Genetic Models

7.3 Some Economic Models

7.4 Some Markov Chain Models

Appendix

Solutions to Problems

References

Index

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Tags: Alexander Graham, Nonnegative Matrices, Applicable Topics, Linear Algebra