School of Mathematics School of Mathematics
Course 113 - Linear Algebra 2007-08 (JF Mathematics
JF Theoretical Physics
JF TSM Mathematics )
Lecturer: Dr. Vladimir Dotsenko

Requirements/prerequisites: None.

Duration: 24 weeks

Number of lectures per week: 3


End-of-year Examination: 3-hour examination


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

Oct 5, 2007

File translated from TEX by TTH, version 2.70.
On 5 Oct 2007, 16:59.