This course covers matrices (including matrix operations, inversion) and systems of linear equations (including their solutions by Gauss elimination and matrix operations). Determinants, co-factors, Cramer’s rule, Euclidean space, general vector spaces, sub-spaces idea, linear independence, dimension, row, column, and null spaces concepts will be introduced. We will also discuss norms, distance ideas, operations such as inner product, concepts of orthogonal bases, and Gram-Schmidt orthogonalization. Eigenvalues, eigenvectors, eigenspaces, eigenbases and their applications will be taught. There will be three special topics which cover quadratic forms, positive definiteness and Least squares solution. In addition, functional language programming will be incorporated such as MatLab and Excel VBA
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