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Algebra Seminar: The Cayley Transform
1:10p.m. Neill 106W
Abstract: The Cayley transform maps a unitary matrix to an Hermitian matrix. Using this transform, I will illustrate how we can learn more about the structure of unitary matrices based on what we know about Hermitian matrices. In particular, I will present a variational characterization of the eigenvalues of a unitary matrix based on the Courant-Fischer theorem for Hermitian matrices. Using the Cayley transform, I will also introduce an algorithm that computes the eigenvalues of a unitary matrix based on an algorithm that computes the eigenavlues of an Hermitian matrix.