Advanced Determinant Calculus

TL;DR

This paper offers tools, examples, and references for evaluating complex determinants, aiding researchers in efficiently handling determinant calculations in various mathematical contexts.

Contribution

It introduces useful tools, compiles evaluated determinants with context, and provides references for further determinant evaluations, enhancing research efficiency.

Findings

Provides efficient tools for determinant evaluation

Lists evaluated determinants with contextual explanations

Offers references for additional determinant evaluations

Abstract

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.