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Linear algebra: course
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This is a one-semester course in linear algebra and vector spaces. An emphasis is made on the coordinate free analysis. The course mimics in some ways a modern algebra course.
Prerequisites
Lectures
- Vector spaces: introduction
- More on vector spaces
- Solving systems of linear equations
- Internal structure of a vector space: part 1
- Internal structure of a vector space: part 2
- Internal structure of a vector space: part 3
- Matrices: part 1
- Matrices: part 2
- Matrices as functions
- Linear operators: part 1
- Linear operators: part 2
- Linear operators: part 3
- Linear operators: part 4
- Linear operators: part 5
- Determinants of linear operators
- Eigenvalues and eigenvectors of linear operators
- Dual spaces
- Diagonalization of matrices
- Inner product spaces: part 1
- Vector space of infinite sequences
- Inner product spaces: part 2
Exercises and tests
- Linear algebra: exercises
- Linear algebra: homework 1
- Differential forms: homework 1
- Linear algebra: test 1
- Linear algebra: test 2
- Linear algebra: final
- Review exercises
Notes
The content came from this complete set of handwritten lectures.
Texts:
The following topics weren't addressed enough:
- quotients, products, etc,
- infinite-dimensional spaces,
- inner products spaces,
- dual spaces,
- eigenvalues and eigenvectors,
or not at all:
- multilinear algebra;
- tensor product;
- vector spaces over general fields, modules.
All are required for serious applications of linear algebra.
