A textbook for a one-semester course in linear algebra for graduate or upper-level undergraduate students of mathematics and engineering. Employs a matrix perspective, and emphasizes training in definitions, theorems, and proofs. Annotation copyright Book News, Inc. Portland, Or.
I. MATRICES AND LINEAR SYSTEMS OF EQUATIONS
1. Matrices
2. Matrix Arithmetic
3. The Multiplication of Partitioned Matrices
4. Gaussian Elimination
5. Elementary Matrices and Inverses 6 LU Factorizations II. VECTOR SPACES
1. Definitions and Examples
2. Finite Dimensional Vector Spaces, Bases, and Dimension
3. The Rank of a Matrix
4. Linear Transformations
5. Matrix Representations of Linear Transformations III. DETERMINANTS
1. Permutations and the Definition of the Determinant
2. Basic Theorems on Determinants
3. The Laplace Expansion
4. Eigenvalues and the Spectrum of a Matrix IV. INNER PRODUCT SPACES
1. Real Inner Product Spaces
2. Complex Inner Product Spaces
3. Least Squares Problems
4. Normal Matrices5. Real Quadratic Forms
William C. Brown, Michigan State University
