Linear Algebra Syllabus |
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General Information | Homework Assignments | |||
This is a tentative syllabus subject to change at the discretion of the instructor without prior notification. This is to give you an idea of the topics I want you to learn.
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Date |
Sections |
Brief Description |
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Week 1 |
1.2, 1.3, 1.4, 1.5 |
Intro to proofs and Vectors spaces, linear dependence and linear independence. |
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Week 2 |
1.6, 2.1, 2.2, 2.3 |
Bases and dimension. Linear transformations, matrix representations of linear transformations. |
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Week 3 |
2.4, 2.5, 2.6, 3.1 |
Isomorphisms. Change of coordinate matrix, dual spaces. Elementary Matrices. |
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Week 4 |
3.2, 3.3, 3.4, 4.1-4.2 |
Rank of a matrix, matrix inverses, systems of linear equations. Determinants. |
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Week 5 |
4.2-4.4, 5.1, 5.2 |
Determinants, Eigenvalues and eigenvectors, diagonalizability. |
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Week 6 |
5.4, 6.1, 6.2 |
Cayley-Hamilton Theorem, Inner producs and Norms, Gram-Schmidt orthogonalization Process |
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Week 7 |
6.3, 6.5 |
The adjoint of a linear operator, unitary and orhogonal operators. |
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Week 8 |
6.6, 6.7 |
Orthogonal projections and spectral theorem, bilinear and quadratic forms. |
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Week 9 |
7.1 |
Jordan Canonical Form. |
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Week 10 |
7.2, 7.3 |
Jordan Canonical Form,
Minimal polynomial. |
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