Difference between revisions of "MAT5283"
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Introduction to the theory of finite-dimensional vector spaces. | Introduction to the theory of finite-dimensional vector spaces. | ||
| − | + | == Sample textbook == | |
[1] M. Thamban Nair · Arindama Singh, ''Linear Algebra'', 2008. Freely available to UTSA students. | [1] M. Thamban Nair · Arindama Singh, ''Linear Algebra'', 2008. Freely available to UTSA students. | ||
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| − | + | == Catalog entry == | |
| − | ''Prerequisite'': | + | ''Prerequisite'': Discrete Mathematics (MAT3003), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent. |
''Contents'' | ''Contents'' | ||
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|| 1.1-1.8 | || 1.1-1.8 | ||
|| Vector space axioms, subspaces, linear independence and bases, dimension, sums and quotients of vector spaces | || Vector space axioms, subspaces, linear independence and bases, dimension, sums and quotients of vector spaces | ||
| − | || | + | || MAT3003, CS2233/2231, or instructor consent. |
|- | |- | ||
| 4-5 | | 4-5 | ||
Latest revision as of 22:04, 25 March 2023
Introduction to the theory of finite-dimensional vector spaces.
Sample textbook
[1] M. Thamban Nair · Arindama Singh, Linear Algebra, 2008. Freely available to UTSA students.
Catalog entry
Prerequisite: Discrete Mathematics (MAT3003), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
Contents (1) Finite-dimensional vector spaces: Vector space axioms, subspaces, linear independence and bases, dimension, sums and quotients of vector spaces (2) Linear transformations: Rank and nullity, isomorphisms, bases, change of basis. (3) Gauss-Jordan elimination: Row operations, echelon forms, determinants. (3) Inner product spaces: Projections, orthogonal bases and Gram-Schmidt, least squares approximation, Riesz representation. (4) Eigenvalues and eigenspaces: Characteristic polynomials, diagonalization. (5) Jordan form, spectral representation.
Topics List
| Week | Topic | Sections from the Nair-Singh book | Subtopics | Prerequisite |
|---|---|---|---|---|
| 1-3 | Finite-dimensional vector spaces | 1.1-1.8 | Vector space axioms, subspaces, linear independence and bases, dimension, sums and quotients of vector spaces | MAT3003, CS2233/2231, or instructor consent. |
| 4-5 | Linear transformations | 2.1-2.6 | Rank and nullity, matrix representation, the space of linear transformations. | |
| 6 | Gauss-Jordan elimination | 3.1-3.7 | Row operations, echelon form and reduced echelon form, determinants. | |
| 7-8 | Inner product spaces | 4.1-4.8 | Projections, orthogonal bases and Gram-Schmidt, least squares approximation, Riesz representation. | |
| 9 | Eigenvalues and eigenvectors | 5.1-5.5 | Eigenspaces, characteristic polynomials | |
| 10 | Canonical forms | 6.1-6.5 | Jordan form | |
| 11-13 | Spectral representation | 7.1-7.6 | Singular value and polar decomposition. |
