Simultaneous symplectic spectral decomposition of positive semidefinite matrices
Abstract
We establish necessary and sufficient conditions on simultaneous symplectic spectral decomposition of a family of 2n × 2n real positive semidefinite matrices with symplectic kernels. We also provide a precise algebraic condition on a 2n × 2n real positive semidefinite matrix with symplectic kernel for orthosymplectic spectral diagonalization, which generalizes a known result for positive definite matrices.
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