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Linear Algebra

Linear algebra is the study of vector spaces and linear operators on them. The canonical example is just standard vectors having matrices applied to them. Given the use of matrices and vectors everywhere in physics, as well as linear operators being particularly nice for mathematicians to consider no one can do a mathematics or physics degree and not cover some form of linear algebra at some point. The simple stuff like the notion of a basis and how to act matrices on vectors is material encountered even before university. However, the more advanced notions like dual spaces, kernels and vector space decompositions are covered at some point in the first or second year of university.

The Cambridge undergraduate mathematics degree, at least around 2002/2003, did an introductory course in the first year and then a more specific indepth course in the second year, before moving onto more specialised parts. The Linear Maths lecture notes provided are a combination of those 1st and 2nd year courses and cover the following;

  • Vector spaces and maps on them
  • Basis, linear combinations, linear operator
  • Linear maps and matrix representations
  • Morphisms
  • Differential equations in vector spaces
  • Vector space decompositions
  • Dual spaces

This is a 1st/2nd year lecture course.

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