Applied Linear Algebra and Matrix Analysis Book

Linear Systems of Equations     1
Some Examples     1
Notation and a Review of Numbers     9
Gaussian Elimination: Basic Ideas     21
Gaussian Elimination: General Procedure     33
Computational Notes and Projects     46
Matrix Algebra     55
Matrix Addition and Scalar Multiplication     55
Matrix Multiplication     62
Applications of Matrix Arithmetic     71
Special Matrices and Transposes     86
Matrix Inverses     101
Basic Properties of Determinants     114
Computational Notes and Projects     129
Vector Spaces     145
Definitions and Basic Concepts     145
Subspaces     161
Linear Combinations     170
Subspaces Associated with Matrices and Operators     183
Bases and Dimension     191
Linear Systems Revisited     198
Computational Notes and Projects     208
Geometrical Aspects of Standard Spaces     211
Standard Norm and Inner Product     211
Applications of Norms and Inner Products     221
Orthogonal and Unitary Matrices     233
Change of Basis and LinearOperators     242
Computational Notes and Projects     247
The Eigenvalue Problem     251
Definitions and Basic Properties     251
Similarity and Diagonalization     263
Applications to Discrete Dynamical Systems     272
Orthogonal Diagonalization     282
Schur Form and Applications     287
The Singular Value Decomposition     291
Computational Notes and Projects     294
Geometrical Aspects of Abstract Spaces     305
Normed Spaces     305
Inner Product Spaces     312
Gram-Schmidt Algorithm     323
Linear Systems Revisited     333
Operator Norms     342
Computational Notes and Projects     348
Table of Symbols     355
Solutions to Selected Exercises     357
References     375
Index     377