Linear Algebra: Concepts and Applications

by D. Kumar

Covers important topics of Linear equations and matrices, Vector spaces, Linear transformations, Matrix analysis, Eigenvalues and eigenvectors and Inner product spaces. This book will help the reader work on the problems of numerical analysis, operations research, differential equations and engineering applications.

Table of Contents

• Preface
• List of Symbols
• Linear Equations and Solution of Linear Equations
• Matrix Inversion
• Partition of Matrices
• Minors and Rank of Matrices
• Cofactor and Adjoint Matrix
• Vector Introduction
• Subspaces
• Span of a Set
• Linear Dependence, Independence
• Bases and Dimension
• Sums of Subspaces
• Linear Variety
• Linear Introduction
• Range and Null Space
• Rank and Nullity of Linear Maps
• Inverse of a Linear Transformation
• The Space L (U,V)
• Composition of Linear Maps
• Operator Equations
• Matrix Matrices Versus Linear Maps
• Sums and Multiplication of Matrix
• Rank and Nullity of a Matrix
• Rank-Factorization and Basic Solutions
• Special Types of Matrices
• Eigenvalues and Introduction
• Properties of Eigenvalues and Eigenvectors
• Diagonalization of Matrices
• Cayley-Hamilton Theorem
• Inner Product Introduction
• Norm
• Orthogonality and Orthonormal Bases
• Orthogonal and Unitary Matrices
• Objective Type Questions
• Bibliography
• Answers
• Index.

254 pages, Hardcover

First published January 1, 2012