Linear Algebra

Preface
Outline
Systems of Equations and Matrices
Introduction
Systems of Equations
Solving Systems of Equations
Matrices
Matrix Arithmetic & Operations
Properties of Matrix Arithmetic and the Transpose
Inverse Matrices and Elementary Matrices
Finding Inverse Matrices
Special Matrices
LU-Decomposition
Systems Revisited
Determinants
Introduction
The Determinant Function
Properties of Determinants
The Method of Cofactors
Using Row Reduction To Compute Determinants
Cramer’s Rule
Euclidean n-Space
Introduction
Vectors
Dot Product & Cross Product
Euclidean n-Space
Linear Transformations
Examples of Linear Transformations
Vector Spaces
Introduction
Vector Spaces
Subspaces
Span
Linear Independence
Basis and Dimension
Change of Basis
Fundamental Subspaces
Inner Product Spaces
Orthonormal Basis
Least Squares
QR-Decomposition
Orthogonal Matrices
Eigenvalues and Eigenvectors
Introduction
Review of Determinants
Eigenvalues and Eigenvectors
Diagonalization