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Bounds on the determinant of an exponential matrix

Michael S. Floater

Abstract

We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.

Bounds on the determinant of an exponential matrix

Abstract

We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.
Paper Structure (7 sections, 4 theorems, 43 equations)

This paper contains 7 sections, 4 theorems, 43 equations.

Table of Contents

  1. Introduction
  2. The case $n=2$
  3. A multiple integral
  4. Proof of the upper bound
  5. Divided difference error formula
  6. Proof of the lower bound
  7. Gaussian matrices

Key Result

Theorem 1

Theorems & Definitions (4)

  • Theorem 1
  • Lemma 1
  • Lemma 2
  • Corollary 1