PreprintCC BY 4.0arXiv
Diagonalization of the Toda flow for arbitrary isospectral symmetric matrices
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 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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BibTeX
@misc{torres2026diagonalization,
title = {{Diagonalization of the Toda flow for arbitrary isospectral symmetric matrices}},
author = {David Martínez Torres and Carlos Tomei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.07263},
eprint = {2608.07263},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.07263},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Diagonalization of the Toda flow for arbitrary isospectral symmetric matrices
AU - David Martínez Torres
AU - Carlos Tomei
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2608.07263
UR - https://arxiv.org/abs/2608.07263
AB - 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 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.
ER -