Linear operators - Mathematical Methods

Mathematical Methods: Linear Operators

This page covers the contents of the second two bursts of lectures (19 and 21 Oct). Topics include:

• Representation of operators by matrices
• Change of basis
• Special types of operator: unitary, Hermitian etc
• Characterising operators: rank, trace, determinant
• Eigenproperties of Hermitian operators: diagonalisation

Here are my notes (2-up) and problems for these topics. (NB: Q8 simplified, 24/10/2011.)

See also sections 9-17 of Fabian Essler’s MT2009 notes and problems 15-19 of his Problem Set I and all of his Problem Set II