- Compute and apply eigenvalues, eigenvectors, and the Jordan decomposition;
- Test matrices for diagonalizability and for positive-definiteness;
- Compute orthogonal bases and use them to solve geometric problems;
- Know basic notions of module theory and some examples of modules;
- Compute and apply the SVD, the Hermite normal form, and the Smith normal form of matrices;
- Also understand longer proofs about linear algebra;
- Also prove nontrivial facts about linear algebra independently;
- Estimate the algorithmic complexity of matrix operations
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Theory of eigenvalues, euclidean vector spaces, elementary module theory, algorithmic aspects of linear algebra.
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