Definite versus Indefinite Linear Algebra

Matrices with symmetries with respect to indefinite inner products arise in many applications, e.g., Hamiltonian and symplectic matrices in control theory and/or the theory of algebraic Riccati equations. In this talk, we give an overview on latest developments in the theory of matrices in indefinite inner product spaces and focus on the similarities and differences to the theory of Euclidean inner product spaces. Topics include normality, polar decompositions, and singular value decompositions in indefinite inner product spaces.

Christian Mehl, Technische Universitaet Berlin, Germany

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