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arXiv · 2108.00223

Optimal unit triangular factorization of symplectic matrices

Pengzhan Jin·Zhangli Lin·Bo Xiao
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Abstract

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 factors. We also show the corresponding improved conclusions for structured subsets of symplectic matrices. This factorization further provides an unconstrained optimization method on $2d$-by-$2d$ real symplectic group (a $2d^2+d$-dimensional Lie group) with $2d^2+3d$ parameters.

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Pengzhan Jin, Zhangli Lin, Bo Xiao. 2021-07-31. Optimal unit triangular factorization of symplectic matrices. https://arxiv.org/abs/2108.00223

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