English

Notes on Linear Algebra

This module is a mixture of abstract theory, with rigorous proofs, and concrete calculations with matrices. The abstract component builds on the notions of subspaces and linear maps to construct the theory of bilinear forms i.e. functions of two variables which are linear in each variable, dual spaces (which consist of linear mappings from the original space to the underlying �eld) and determinants. The concrete applications involve ways to reduce a matrix of some speci�c type (such as symmetric or skew-symmetric) to as near diagonal form as possible.

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