Linear Algebra with Applications

This book gives a self- contained treatment of linear algebra with many of its most important applications. It is very unusual if not unique in being an elementary book which does not neglect arbitrary fields of scalars and the proofs of the theorems. It will be useful for beginning students and also as a reference for graduate students and others who need an easy to read explanation of the important theorems of this subject.

It presents a self- contained treatment of the algebraic treatment of linear differential equation which includes all proofs. It also contains many different proofs of the Cayley Hamilton theorem. Other applications include difference equations and Markov processes, the latter topic receiving a more thorough treatment than usual, including the theory of absorbing states. In addition it contains a complete introduction to the singular value decomposition and related topics like least squares and the pseudo-inverse.

Most major topics receive more than one discussion, one in the text and others being outlined in the exercises. The book also gives directions for using maple in performing many of the difficult algorithms.

Contents:

• Numbers, Vectors and Fields
• Matrices
• Row Operations
• Vector Spaces
• Linear Mappings
• Inner Product Spaces
• Similarity and Determinants
• Characteristic Polynomial and Eigenvalues of a Matrix
• Some Applications
• Unitary, Orthogonal, Hermitian and Symmetric Matrices
• The Singular Value Decomposition

Readership: Undergraduates in linear algebra.
Key Features:

• This book proves all the theorems including theorems about the determinant
• This book does not neglect algebraic considerations like general fields
• The applications of linear algebra are given a reasonably complete development