| Weeks | Topics |
| 1 |
Two-dimensional, Three-dimensional, and n-dimensional vectors; Linear combinations, Inner (scalar) product; Norm of a vector; Cross product.
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| 2 |
Projection of a vector on a vector; Planes; Sample problem solutions.
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| 3 |
Linear equation systems; Solution of linear equation systems: Gauss elimination method.
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| 4 |
Matrices; Matrix operations.
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| 5 |
Computation of matrix inverse: Gauss-Jordan elimination method; Determinant of a matrix.
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| 6 |
Implementing Gauss elimination method with elimination matrices; Matrix decomposition: LU and LDLT decomposition.
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| 7 |
Vector spaces and subspace concept; Four fundamental subspaces for a matrix; Rank of a matrix; The solution of an underdetermined linear equation system
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| 8 |
Linear independence; Vectors spanning a subpace; Bases of a vector space; Dimensions of a vector space.
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| 9 |
Inner product spaces; Orthogonal vectors and orthogonal subpaces
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| 10 |
Projection on subspaces: Solution of overdetermined linear systems of equations; Least squares approximation. Gram-Schmidt orthogonalization (GSO) method.
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| 11 |
Eigenvalues and eigenvectors for matrices; Diagonalization.
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| 12 |
Diagonalization of symmetric matrices; Solution of difference and differential equations.
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| 13 |
Singular Value Decomposition (SVD): Decomposition method of m × n matrices for m≠ n.
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| 14 |
Pseudo-inverse of a matrix, Applications: Image processing and effective rank computation
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