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arXiv · 2412.01492

Simultaneous symplectic spectral decomposition of positive semidefinite matrices

Rudra R. Kamat·Hemant K. Mishra
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Abstract

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

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Rudra R. Kamat, Hemant K. Mishra. 2024-12-02. Simultaneous symplectic spectral decomposition of positive semidefinite matrices. https://doi.org/10.1016/j.laa.2026.02.023

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