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Volume 10, Issue 3, Article 63 |
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An Upper Bound for the Determinant of a Matrix with given Entry Sum and Square Sum
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Authors: |
Ortwin Gasper, Hugo Pfoertner, Markus Sigg, |
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Keywords:
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Determinant, Matrix Inequality, Hadamard's Determinant Theorem, Hadamard Matrix. |
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Date Received:
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05/03/2009 |
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Date Accepted:
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15/09/2009 |
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Subject Codes: |
15A15, 15A45, 26D07.
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Editors: |
Sever S. Dragomir, |
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Abstract: |
By deducing characterisations of the matrices which have maximal determinant in the set of matrices with given entry sum and square sum, we prove the inequality  for real  -matrices  , where  and  are the sum of the entries and the sum of the squared entries of , respectively, and  , provided that  . This result is applied to find an upper bound for the determinant of a matrix whose entries are a permutation of an arithmetic progression.
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