Nonnegative Matrices and Applicable Topics in Linear Algebra (Dover Books on Mathematics)

Title Page
Copyright Page
Contents
Preface
Examples of Notation Used
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 PerronFrobenius 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