Optimal unit triangular factorization of symplectic matrices


Abstract in English

We prove that any symplectic matrix can be factored into no more than 5 unit triangular symplectic matrices, moreover, 5 is the optimal number. This result improves the existing triangular factorization of symplectic matrices which gives proof of 9 blocks. We also show the corresponding improved conclusions for structured subsets of symplectic matrices.

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