Mathematical Sciences: Collaboration in Matrix Analysis

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The research in this project is concerned with the theory of matrices and operators. The problems under consideration include matrix completion problems; determinantal inequalities for positive definite matrices; algebraic Riccati equations; interpolation for rational matrix functions; qualitative matrix theory; spectral assignment in infinite dimensions; and interpolation of strong forms of nonsingularity. A matrix is a rectangular array of objects. Given two matrices there is a notion of how to add them and how to multiply them. This rather general setting turns out to be very useful in describing situations which arise in many areas of science. This project is concerned with the theory of matrices.