Further Linear Algebra – LSE


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Topics covered

  • Diagonalisation and Jordan normal form, applied to systems of differential equations.
  • Inner products, orthogonality, quadratic forms, and orthogonal diagonalisation.
  • Direct sums and projections, with applications to least squares.
  • Generalized inverses.
  • Complex numbers. Complex matrices and vector spaces. Hermitian and unitary matrices, unitary diagonalisation and spectral decomposition.

Learning outcomes

If you complete the course successfully, you should be able to:

  • Knowledge of the concepts, terminology, techniques and conventions covered in the half course.
  • The ability to demonstrate an understanding of the underlying principles of the subject.
  • The ability to demonstrate the ability to solve unseen mathematical problems involving an understanding of the concepts.


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