Systems of Equations; Augmented Matrices and Elementary Row Operations; The Algebra of Matrices; Invernesses of Matrices; Determinants, Adjoints and Cramer's Rule; Matrix Algebra and Modular Arithmetic; Vector Products, Lines and Planes; Vector Spaces and Subspaces; Independence, Basis and Dimension; Row Space, Column Space and Null Space; Inner Product Spaces; Orthonormal Bases and the Gram-Schmidt Process; Change of Basis and Orthogonal Matrices; Eigenvalues and Eigenvectors; Diagonalization and Orthogonal Diagonalization; Matrices and Linear Transformations from RN to RM; Matrices of General Linear Transformation Similarity; Applications and Numerical Methods.
