Ryan Takahashi

Harvey Mudd College Mathematics 2013

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Thesis Proposal: Displacement Operators
Thesis Advisor: Prof. Michael Orrison
Second Reader: Prof. Nicholas Pippenger
E-Mail: rtakahashi@g.hmc.edu

Structured Matrices and the Algebra of Displacement Operators

Matrix calculations underlie countless problems in science, mathematics, and engineering. When the involved matrices are highly structured, displacement operators can be used to accelerate fundamental operations such as matrix-vector multiplication. In this thesis, we provide an introduction to the theory of displacement operators and study the interplay between displacement and natural matrix constructions involving direct sums, Kronecker products, and blocking. We also investigate the algebraic behavior of displacement operators, developing results about invertibility and kernels.