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arXiv · 2608.07263

Diagonalization of the Toda flow for arbitrary isospectral symmetric matrices

David Martínez Torres·Carlos Tomei
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Abstract

We construct coordinates on orthogonal conjugacy classes of traceless real symmetric matrices with arbitrary spectrum (the isospectral manifold) that diagonalize the non-periodic Toda vector field. The coordinates, defined on a neighborhood of any diagonal matrix decouple the Toda vector field into a sum of multiples of the Euler vector field in $\mathbb{R}$. The domain of each set of coordinates is dense and their union covers the isospectral manifold. The construction relies on a new matrix factorization which is of independent interest.

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David Martínez Torres, Carlos Tomei. 2026-08-07. Diagonalization of the Toda flow for arbitrary isospectral symmetric matrices. https://arxiv.org/abs/2608.07263

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