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Further linear algebra MT2175

Half course

In MT1173 Algebra, students have met many of the key concepts of linear algebra. In this course, we study further theoretical material and look at additional applications of linear algebra.

Prerequisites/ exclusions

Prerequisite: A course that you must have ordinarily attempted all elements of before you are permitted to register for another particular course.

If taken as part of a BSc degree, courses which must be attempted before this half course may be taken:

  • MT1173 Algebra

This half course may not be taken with MT3095 Further mathematics for economists.

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.


Unseen written examination (2 hrs). 

Essential reading

  • Anthony, M. and M. Harvey. Linear Algebra: Concepts and Methods. Cambridge University Press.

Course information sheets

Download the course information sheets from the LSE website.