JF Theoretical Physics

JF TSM Mathematics )

**Requirements/prerequisites:** None.

**Duration:** 24 weeks

**Number of lectures per week:** 3

**Assessment:**

**End-of-year Examination:** 3-hour examination

**Description: **

- Systems of simultaneous linear equations. Examples.
- Gauss-Jordan elimination. Fredholm's alternative. Applications.
- Numerical methods in linear algebra. LU-decomposition.
- Determinants. Permutation groups.
- Cramer's rule for systems of linear equations.
- Coordinate vector space.
- Fields: rationals, reals, and complex.
- Abstract vector spaces.
- Linear independence: criteria.
- Bases and dimensions.
- Linear operators. Matrices.
- Change of basis.
- Characteristic polynomials.
- Eigenvalues and eigenvectors. Diagonalisation of a semisimple operator.
- Cayley-Hamilton theorem. Minimal polynomial of a linear operator.
- Normal form for a nilpotent operator. Jordan normal form.
- Bilinear Forms.
- Orthonormal bases; Gram-Schmidt orthogonalisation procedure.
- Spectral Theorem for symmetric/Hermitian/normal operators.

Oct 5, 2007

File translated from T

On 5 Oct 2007, 16:59.