MAT5283

Introduction to the theory of finite-dimensional vector spaces.

Catalog entry

Prerequisite: Prerequisite: Math 2233 Linear Algebra, Math 2243 Applied Linear Algebra or instructor approval. , or instructor consent.

Contents: (1) Algebraic Structures: rings, matrices, polynomials, fields and finite fields (2) Vector spaces: subspaces, linear independence, basis, dimension (3) Linear transformations, isomor- phisms, Rank-Nullity Theorem, Product and Quotient Spaces (3) Matrices and Linear Transfor- mations: Matrix representation, change of basis, equivalence of matrices, similarity (4) Eigen- values and Eigenvectors: The Cayley-Hamilton Theorem, Diagonalization and Jordan Canoni- cal forms (4) Real and Complex Inner Product Spaces: Norm, distances, Cauchy-Schwartz in- equality, Gram-Schmidt Orthogonalization process, The Projection Theorem, Riez Representa- tion Theorem (5) Orthogonality over finite fields (6) Multilinear algebra : Bilinear Forms and Functionals, Tensor product of vector spaces and Matrices.