Speaker: Greg Friedman, Texas Christian University

Title: Topological linear algebra - the unitary equivalence of matrices over topological spaces

(joint with Efton Park, Texas Christian University)

Abstract: As an application of topology to linear algebra, we study the question of unitary equivalence for matrices with coefficients in the ring C(X) of continuous complex-valued functions over a topological space X (equivalently, one can imagine a family of matrices that varies continuously over the points of X). If X is a CW complex and A and B are normal matrices over C(X) with the same set of distinct eigenvalues, we show that there is a single cohomological obstruction that completely determines whether A and B are unitary equivalent. Using this tool, it is often possible to count or bound the number of unitary equivalence classes on X with given eigenvalues. This generalizes work of Grove and Pedersen on the diagonalizability of normal matrices with coefficients in C(X).

Engineering and Computer Science West (ECSW), 1.315
800 W. Campbell Road, Richardson, Texas 75080-3021

Natural Sciences & Mathematics
Stephen E. McKeown

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