Overview
Description
Vector spaces; duality, direct sums; linear maps: eigenvalues, eigenvectors, rational and Jordan forms; bilinear maps, quadratic forms; inner product spaces: symmetric, skewsymmetric, orthogonal maps, spectral theorem.
Units
Lecture3
Catalog Details
Offering
Offered: Every Fall - Odd Years
Terms
fall
Attributes
Standard
Learning Outcomes
- demonstrate understanding of the vocabulary of Linear Algebra at an advanced level.
- demonstrate competence at an advanced level by rigorously proving results from Linear Algebra I.
- work with self-adjoint, normal and positive operators on inner product spaces.
- work with special decompositions and forms of matrices: e.g. the singular value decomposition, Jordan form.