Determinants of Block Tridiagonal Matrices

TL;DR

This paper proves a mathematical identity that simplifies the calculation of determinants for block tridiagonal matrices by relating them to transfer matrices, aiding in computational and theoretical analysis.

Contribution

It introduces a new identity linking block tridiagonal determinants to transfer matrices, enhancing understanding and computation.

Findings

Determinant of block tridiagonal matrices can be evaluated via transfer matrices.

The identity applies to matrices with or without corner modifications.

Provides a new tool for analyzing structured matrices in various applications.

Abstract

An identity is proven that evaluates the determinant of a block tridiagonal matrix with (or without) corners as the determinant of the associated transfer matrix (or a submatrix of it).