- Rings. Ring of polynomials and its ideal structure.
The prime factorization of a polynomial. Lagrange interpolation.
- Eigenvalues and eigenvectors of linear operators.
- Characteristic polynomial and Cayley-Hamilton theorem. The primary decomposition theorem.
Diagonalization. Nilpotent operators. Jordan decomposition in small dimension Jordan decomposition in general dimension- time permitted
- Linear forms. Dual basis. Bilinear forms.
- Inner product spaces. Orthogonal bases. Projections. Adjoint linear transformation. Unitary and Hermitian operators.
- Normal operators and the spectral decomposition theorem. Singular value decomposition theorem and applications.
- University course catalogue:
- First Year
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