- The geometry of Linear equations, Elimination with Matrices, Multiplication and Inverse Matrices, Factorization into A= LU, Transposes, Pamutations, spaces R^n, Column Space and Null Space, Solving Ax = 0; Pivot variables, Special Solutions, Solving Ax = 0; row reduced form R, Independence, bases and dimension, The four fundamental subspaces, Matrix Spaces; rank 1, Small world graphs, Graphs networks, Incidence matrices, Orthogonal vectors and subspaces, Projections onto subspaces, Projection matrices and least quares, Orthogonal matrices and Gram-Schmidt, Properties of determinants, Determinant formulas and cofactors, Cramer's rule, Inverse matrices and Volume, Eigenvalues and Eigenvectors, Diagonalization and powers of A, Differential equations and exp(At), Markov matrices; Fourier Series, Symmetric matrices and positive definiteness, Complex matrices; Fast fourier transform, Positive definite matrices and minima, Similar Matrices and Jordan form, Singular value decomposition, Linear transformations and their matrices, Change of basis, Image Compression, Left and Right inverses; Pseudoinverse.
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