CH1-8 LDU factorization

CH2-1 Basic Properties of the determinants

CH2-2 Existence and uniqueness of the determinant

CH2-3 Cofactor expansion

CH2-4 Cramer's rule

CH3-1 The n-space R^n and vector space

CH3-2 Subspaces

CH3-3 Bases

CH3-4 Dimensions

CH3-5 Row and column spaces

CH3-6 Rank and nullity

CH3-7 Bases for subspaces

CH3-8 Invertibility

CH4-1 Basic Properties of a linear transformation

CH4-2 Invertible linear transformations

CH4-3 Matrices of a linear transformations

CH4-4 Vector spaces of a linear transformations

CH4-5 Change of bases

CH4-6 Similarity

CH5-1 Dot products and inner products

CH5-2 The lengths and angles of vectors

CH5-3 Matrix representations of inner products

CH5-4 Orthogonal projections

CH5-5 The Gram-Schmidt orthogonalization

CH5-6 Relations of fundamental subspaces

CH5-7 Orthogonal matrices and isometries

CH6-1 Eigenvalues and eigenvectors

CH6-2 Diagonalization of matrices

CH6-4 Exponential Matrices

CH6-6 Diagonalization of linear transformations

CH7-1 The n-space C^n and complex vector spaces

CH7-2 Hermitian and unitary matrices

CH7-3 Unitarily diagonalizable matrices

CH7-4 Normal matrices

CH8-1 Jordan Canonical Forms

CH8-2 Generalized eigenvectors

CH8-3 The power A^k and the exponential e^A

CH8-4 Cayley-Hamilton theorem

CH8-5 The minimal polynomial of a matrix