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Hadamard's Determinant Inequality.

Kenneth Lange1

  • 1Departments of Biomathematics, Human Genetics, and Statistics, University of California, Los Angeles, CA 90095.

The American Mathematical Monthly : the Official Journal of the Mathematical Association of America
|October 7, 2014
PubMed
Summary
This summary is machine-generated.

This study presents a concise and elementary proof for Hadamard's determinant inequality. This fundamental result has broad applications in linear algebra and matrix theory.

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Area of Science:

  • Mathematics
  • Linear Algebra
  • Matrix Theory

Background:

  • Hadamard's determinant inequality is a significant result in matrix theory.
  • Existing proofs may be complex or lengthy.

Purpose of the Study:

  • To provide a short and elementary proof of Hadamard's determinant inequality.
  • To make this important theorem more accessible to a wider audience.

Main Methods:

  • The proof utilizes basic concepts from linear algebra.
  • The method focuses on simplicity and directness.

Main Results:

  • A novel, elementary proof of Hadamard's determinant inequality is established.
  • The proof is significantly shorter and more accessible than previous methods.

Conclusions:

  • The presented proof simplifies the understanding and application of Hadamard's determinant inequality.
  • This work contributes to the accessibility of fundamental mathematical theorems.