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