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Linear Algebra INF
(Year: 1 Period: 4 Category: Compulsory )
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Course Objectives:
- 1. (understand)represent points, lines and planes in linear algebra, and quantitatively name, calculate and sketch their geometric properties (distances, directions, intersections) (H1)
- 2. (understand)formulate and solve linear equations, albeit exactly with Gaussian elimination (H2). or in least squares sense (H7). In low-dimensional cases, the student can write and solve the linear equations by hand
- 3. (understand)explain the basic operations and basic algorithms of linear algebra, and perform them by hand (in low-dimensional cases). These are Gaussian elimination (H2), matrix multiplication (H3), calculation of the subspaces of a transformation (core and column space H3), calculation of the inverse (if possible H3), orthogonalization (Gram-Schmidt GS, H5), determinant calculation ( H4), diagonalize (if possible, H4), eigenanalysis (H4), bring quadratic forms onto principal axes (H5) and determine the SVD of a matrix (H7)
- 4. (understand)recognize and characterize the most important forms of transformations through their properties (orthogonal transformations H3, H5, orthogonal projections H5, symmetric transformations and quadratic forms H5, general transformations)
- 5. (understand)determine the four subspaces of a linear transformation from its matrix, in low-dimensional cases by hand (H3). The student can relate these subspaces (core, column space/image, core of transpose, column space/image of transpose) to the SVD (H7)
- 6. (understand)explain what determinants mean geometrically, use their algebraic properties in calculations, and perform the Laplace expansion by hand in low-dimensional cases (H4)
- 7. (understand)mastered least squares optimization (LSQ), in theory and practice, as evidenced by being able to recognize LSQ in fitting problems, translate them to LA, and solve low-dimensional fitting problems by hand (H7)
- 8. (understand)relate the three methods of linear algebra: geometric, algebraic and computational (Poole)