This course contains an abstract treatment of finite
dimensional vector
spaces, linear transformations and their invariants.
PREREQUISITES
MATH 240 or MATH 461
TOPICS
Review of basic Linear algebra
Abstract vector spaces
Bases and dimension
Coordinates
Subspaces
Linear transformations
Representation of transformations by matrices
Rank and nullity
Linear functionals and duality Determinants
Definition and properties
Permutation groups
Evaluation Decompositions
Direct sum decompositionss
Invariant subspaces
Eigenvalues and eigenvectors
Characteristic and minimal polynomial
Diagonalizable operators
Primary decompositions
Rational and Jordan canonical forms Inner Product Spaces
Orthonormal Bases
Adjoints
Positive, unitary and normal operators
The spectral theorem
