Contents

• Vector spaces

• Subspaces

• Linear independence and span

• Bases and dimension

• Isomorphism and coordinate representation

• Inner product and norm

• Angles and orthogonality

• Gram-Schmidt orthogonalisation process

• Orthogonal projection and best approximation

• Linear transformations

• Matrix representation of linear transformations

• Change of basis and similarity

• Matrices as linear transformations

• Eigenvalues and eigenvectors

• The characteristic polynomial

• Matrix diagonalisation

• Matrix exponential function

A short summary of linear

algebra and matrix theory

Dr I M Jaimoukha