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Advanced Determinant Calculus

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arxiv math/9902004 v3 pith:PRV5HUVV submitted 1999-02-01 math.CO math-phmath.CAmath.MPmath.NTmath.RA

classification math.COmath-phmath.CAmath.MPmath.NTmath.RA
keywords determinantdeterminantsshouldadvancedalreadyappearappearedarticle
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The purpose of this article is threefold. First, it provides the reader with a few useful and efficient tools which should enable her/him to evaluate nontrivial determinants for the case such a determinant should appear in her/his research. Second, it lists a number of such determinants that have been already evaluated, together with explanations which tell in which contexts they have appeared. Third, it points out references where further such determinant evaluations can be found.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Two-dimensional Toda--Arnoldi correspondence: Holomorphic Krylov geometry and counterdiabatic transport

    quant-ph 2026-08 conditional novelty 5.0 of 10

    For non-Hermitian Hamiltonians, the Arnoldi diagonal and subdiagonal coefficients are the Flaschka variables of the finite two-dimensional Toda lattice, and their squares give both the Fubini-Study metric and the Berr...

  2. Toeplitz Determinants and Admissible Correlation Intervals

    math.PR 2026-06 unverdicted novelty 5.0 of 10

    Derives determinantal formula for admissible correlation interval widths via Desnanot-Jacobi identity on Toeplitz matrices, recovering Schneider & Hartlap (2009) product expressions.

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