Course topics

  • 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.

Course Information

University course catalogue:
201.1.1221
Level:
First Year
Credits:
5.0

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