Published by: ay_lotfy (Karma: 146.67) on 5 October 2015 | Views: 4001
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This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
Course Features 1 The Geometry of Linear Equations 2 Elimination with Matrices 3 Multiplication and Inverse Matrices 4 Factorization into A = LU 5 Transposes, Permutations, Spaces R^n 6 Column Space and Nullspace 7 Solving Ax = 0: Pivot Variables, Special Solutions 8 Solving Ax = b: Row Reduced Form R 9 Independence, Basis, and Dimension 10 The Four Fundamental Subspaces 11 Matrix Spaces; Rank 1; Small World Graphs 12 Graphs, Networks, Incidence Matrices 13 Quiz 1 Review 14 Orthogonal Vectors and Subspaces 15 Projections onto Subspaces 16 Projection Matrices and Least Squares 17 Orthogonal Matrices and Gram-Schmidt 18 Properties of Determinants 19 Determinant Formulas and Cofactors 20 Cramer's Rule, Inverse Matrix, and Volume 21 Eigenvalues and Eigenvectors 22 Diagonalization and Powers of A 23 Differential Equations and exp(At) 24 Markov Matrices; Fourier Series 24b Quiz 2 Review 25 Symmetric Matrices and Positive Definiteness 26 Complex Matrices; Fast Fourier Transform 27 Positive Definite Matrices and Minima 28 Similar Matrices and Jordan Form 29 Singular Value Decomposition 30 Linear Transformations and Their Matrices 31 Change of Basis; Image Compression 32 Quiz 3 Review 33 Left and Right Inverses; Pseudoinverse 34 Final Course Review
