INTRODUCTION TO MATRIX THEORY

Preface
Contents
About the Author
1 Matrix Operations
	1.1 Examples of Linear Equations
	1.2 Basic Matrix Operations
	1.3 Transpose and Adjoint
	1.4 Elementary Row Operations
	1.5 Row Reduced Echelon Form
	1.6 Determinant
	1.7 Computing Inverse of a Matrix
	1.8 Problems
2 Systems of Linear Equations
	2.1 Linear Independence
	2.2 Determining Linear Independence
	2.3 Rank of a Matrix
	2.4 Solvability of Linear Equations
	2.5 Gauss–Jordan Elimination
	2.6 Problems
3 Matrix as a Linear Map
	3.1 Subspace and Span
	3.2 Basis and Dimension
	3.3 Linear Transformations
	3.4 Coordinate Vectors
	3.5 Coordinate Matrices
	3.6 Change of Basis Matrix
	3.7 Equivalence and Similarity
	3.8 Problems
4 Orthogonality
	4.1 Inner Products
	4.2 Gram–Schmidt Orthogonalization
	4.3 QR-Factorization
	4.4 Orthogonal Projection
	4.5 Best Approximation and Least Squares Solution
	4.6 Problems
5 Eigenvalues and Eigenvectors
	5.1 Invariant Line
	5.2 The Characteristic Polynomial
	5.3 The Spectrum
	5.4 Special Types of Matrices
	5.5 Problems
6 Canonical Forms
	6.1 Schur Triangularization
	6.2 Annihilating Polynomials
	6.3 Diagonalizability
	6.4 Jordan Form
	6.5 Singular Value Decomposition
	6.6 Polar Decomposition
	6.7 Problems
7 Norms of Matrices
	7.1 Norms
	7.2 Matrix Norms
	7.3 Contraction Mapping
	7.4 Iterative Solution of Linear Systems
	7.5 Condition Number
	7.6 Matrix Exponential
	7.7 Estimating Eigenvalues
	7.8 Problems
Appendix
Index