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- Title
The Entry Sum of the Inverse Cauchy Matrix.
- Authors
Grinberg, Darij
- Abstract
The article discusses the Cauchy matrix and its various properties and applications. It presents a theorem and provides a new proof for it, along with a lemma that aids in the proof. The text also discusses a mathematical proof involving matrices and summation notation, demonstrating a property of matrix multiplication. It introduces Theorem 1, which states that the sum of all entries of the inverse matrix is equal to the sum of all entries of the original matrix. The text also mentions a variant of Theorem 1 and introduces Theorem 4, which relates to a modified matrix. Additionally, the text discusses a theorem and its proof sketch regarding the calculation of determinants. It concludes with propositions regarding the inverse and determinant of a matrix obtained from another matrix by replacing certain elements. The text also includes a note from the publisher expressing neutrality.
- Subjects
MATRIX inversion; REPRESENTATIONS of groups (Algebra); VANDERMONDE matrices; LINEAR algebra; MATRIX multiplications
- Publication
Mathematical Intelligencer, 2024, Vol 46, Issue 1, p46
- ISSN
0343-6993
- Publication type
Article
- DOI
10.1007/s00283-023-10268-4