MATH 570

Overview

Matrix arithmetic and Linear transformations, The theory of determinants , Rank of a matrix and elementary matrices, Spectral theory, Shur's theorem, Quadratic forms and second derivative test, Gerschgorin's theorem, Abstract vector spaces and general fields, Axioms, Subspaces and bases, Matrix of a linear transformation, Rotations, Eigenvalues and eigenvectors of linear transformations, Jordan Cannonical form and applications, Cayley Hamilton theorem, Markov chains, Regular Markov matrices, Inner product spaces, Gramm Schmidt process, Tensor product of vectors, Least squares, Fredholm alternative, Determinants and volume, Self adjoint operators, Simultaneous diagonalization, Spectral theory, Singular value decomposition, The Frobenius norm, Least squares and the Moore Penrose inverse, Norms for finite dimensional vector spaces, The p norms,

Learning Outcomes

The minimal learning outcomes section of the Math 570 Wiki page outlines material which all students in Math 570 should understand. As evidence of that understanding, students should be able to demonstrate mastery of relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems.