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• WEEK 1:INTRODUCTION TO VECTORS: VECTORS AND LINEAR COMBINATIONS, LENGTHS AND DOT PRODUCTS, MATRICES.
• WEEK 2:SOLVING LINEAR EQUATIONS: VECTORS AND LINEAR EQUATIONS, THE IDEA OF ELIMINATION, ELIMINATION USING MATRICES..
• WEEK 3:RULES FOR MATRIX OPERATIONS, INVERSE MATRICES
• WEEK 4: ELIMINATION = FACTORIZATION; A = LU, TRANSPOSES AND PERMUTATIONS
• WEEK 5: VECTOR SPACES AND SUBSPACES: SPACES OF VECTORS, THE NULL SPACE OF A: SOLVING AX = 0, THE RANK AND THE ROW REDUCED FORM, THE COMPLETE SOLUTION TO AX = B
• WEEK 6:INDEPENDENCE, BASIS AND DIMENSION, DIMENSIONS OF THE FOUR SUBSPACES.
• WEEK 7:ORTHOGONALLY: ORTHOGONALLY OF THE FOUR SUBSPACES, PROJECTIONS.
• WEEK 8: LEAST SQUARES APPROXIMATIONS ,ORTHOGONAL BASES AND GRAM-SCHMIDT.
• WEEK 9: MID TERM EXAM
• WEEK 10: DETERMINANTS: THE PROPERTIES OF DETERMINANTS, PERMUTATIONS AND COFACTORS, CRAMER'S RULE, INVERSES, AND VOLUMES.
• WEEK 11: EIGENVALUES AND EIGENVECTORS: INTRODUCTION TO EIGENVALUES, DIAGONALIZING A MATRIX, APPLICATIONS TO DIFFERENTIAL EQUATIONS
• WEEK 12:SYMMETRIC MATRICES, POSITIVE DEFINITE MATRICES, SIMILAR MATRICES, SINGULAR VALUE DECOMPOSITION (SVD).
• WEEK 13: APPLICATIONS: MATRICES IN ENGINEERING, GRAPHS AND NETWORKS, MARKOV MATRICESPOPULATION, AND ECONOMICS; LINEAR PROGRAMMING.
• WEEK 14: FOURIER SERIES: LINEAR ALGEBRA FOR FUNCTIONS
• WEEK 15:LINEAR ALGEBRA FOR STATISTICS AND PROBABILITY, COMPUTER GRAPHICS.
• WEEK 16:NUMERICAL LINEAR ALGEBRA: GAUSSIAN ELIMINATION IN PRACTICE, NORMS AND CONDITION NUMBERS, ITERATIVE METHODS FOR LINEAR ALGEBRA.
• WEEK 17:COMPLEX VECTORS AND MATRICES: COMPLEX NUMBERS, HERMITIAN AND UNITARY MATRICES, MATRIX FACTORIZATIONS.
• WEEK 18: FINAL EXAM