e to the A, in a New Way

TL;DR

This paper presents explicit formulas for computing the exponential of Hermitian matrices in small dimensions and applies these to derive Fourier transforms of matrix exponentials.

Contribution

It introduces new explicit expressions for matrix exponentials in low dimensions and connects them to Fourier transforms of these exponentials.

Findings

Explicit formulas for exp(A) for 2x2, 3x3, 4x4 Hermitian matrices.

Derived formulas for Fourier transforms of exp(iA).

Provides computational tools for matrix exponentials and their Fourier transforms.

Abstract

Apparently new expressions are given for the exponential of a hermitian matrix,A, in the 2x2,3x3,and 4x4 cases. Replacing A by iA these are explicit formulas for the Fourier transform of exp(iA).