



Volume 10, Issue 3, Article 63 






An Upper Bound for the Determinant of a Matrix with given Entry Sum and Square Sum



Authors: 
Ortwin Gasper, Hugo Pfoertner, Markus Sigg, 



Keywords:

Determinant, Matrix Inequality, Hadamard's Determinant Theorem, Hadamard Matrix. 



Date Received:

05/03/2009 



Date Accepted:

15/09/2009 



Subject Codes: 
15A15, 15A45, 26D07.




Editors: 
Sever S. Dragomir, 









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.
















