Linear Algebra : Course Notes : Edition 1.0 : with table of contents

COVER
TITLE PAGE
TABLE OF CONTENTS
A Note to Students -- READ THIS!
ACKNOWLEDGMENTS
1  VECTORS IN EUCLIDEAN SPACE
	1.1  Vector Addition and Scalar Multiplication
	1.2  Subspaces
	1.3  Dot Product
	1.4  Projections
2  SYSTEMS OF LINEAR EQUATIONS
	2.1  Systems of Linear Equations
	2.2  Solving Systems of Linear Equations
3  MATRICES AND LINEAR MAPPINGS
	3.1  Operations on Matrices
	3.2  Linear Mappings
	3.3  Special Subspaces
	3.4  Operations on Linear Mappings
4  VECTOR SPACES
	4.1  Vector Spaces
	4.2  Bases and Dimension
	4.3  Coordinates
5  INVERSES AND DETERMINANTS
	5.1  Matrix Inverses
	5.2  Elementary Matrices
	5.3  Determinants
	5.4  Determinants and Systems of Equations
	5.5  Area and Volume
6  DIAGONALIZATION
	6.1  Matrix of a Linear Mapping, Similar Matrices
	6.2  Eigenvalues and Eigenvectors
	6.3  Diagonalization
	6.4  Powers of Matrices
7  FUNDAMENTAL SUBSPACES
	7.1  Bases of Fundamental Subspaces
	7.2  Subspaces of Linear Mappings
8  LINEAR MAPPINGS
	8.1  General Linear Mappings
	8.2  Rank-Nullity Theorem
	8.3  Matrix of a Linear Mapping
	8.4  Isomorphisms
9  INNER PRODUCTS
	9.1  Inner Product Spaces
	9.2  Orthogonality and Length
	9.3  The Gram-Schmidt Procedure
	9.4  General Projections
	9.5  The Fundamental Theorem
	9.6  The Method of Least Squares
10  APPLICATIONS OF ORTHOGONAL MATRICES
	10.1  Orthogonal Similarity
	10.2  Orthogonal Diagonalization
	10.3  Quadratic Forms
	10.4  Graphing Quadratic Forms
	10.5  Optimizing Quadratic Forms
	10.6  Singular Value Decomposition
11  COMPLEX VECTOR SPACES
	11.1  Complex Number Review
	11.2  Complex Vector Spaces
	11.3  Complex Diagonalization
	11.4  Complex Inner Products
	11.5  Unitary Diagonalization
	11.6  Cayley-Hamilton Theorem