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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.09883 |
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| _version_ | 1866908954328563712 |
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| author | Younes, Charbel Abi Trogdon, Thomas |
| author_facet | Younes, Charbel Abi Trogdon, Thomas |
| contents | We study the direct and inverse spectral theory for a class of finite Hermitian banded matrices. Using the theory of matrix orthogonal polynomials, we provide an explicit procedure for reconstructing a banded matrix from a matrix-valued measure that encodes its spectral data. We establish necessary and sufficient conditions for a measure to be the spectral measure of a matrix in the examined class. We further analyze the connections between this spectral analysis, block tridiagonalization algorithms, and the Toda lattice evolution on banded matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09883 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Banded Hermitian Matrices, Matrix Orthogonal Polynomials, and the Toda Lattice Younes, Charbel Abi Trogdon, Thomas Spectral Theory Mathematical Physics 42C05, 15B57 We study the direct and inverse spectral theory for a class of finite Hermitian banded matrices. Using the theory of matrix orthogonal polynomials, we provide an explicit procedure for reconstructing a banded matrix from a matrix-valued measure that encodes its spectral data. We establish necessary and sufficient conditions for a measure to be the spectral measure of a matrix in the examined class. We further analyze the connections between this spectral analysis, block tridiagonalization algorithms, and the Toda lattice evolution on banded matrices. |
| title | Banded Hermitian Matrices, Matrix Orthogonal Polynomials, and the Toda Lattice |
| topic | Spectral Theory Mathematical Physics 42C05, 15B57 |
| url | https://arxiv.org/abs/2604.09883 |