A BOUND FOR THE DETERMINANT OF CERTAIN HADAMARD-PRODUCTS AND FOR THE DETERMINANT OF THE SUM OF 2 NORMAL MATRICES

Authors
DRURY SW
Citation
Sw. Drury, A BOUND FOR THE DETERMINANT OF CERTAIN HADAMARD-PRODUCTS AND FOR THE DETERMINANT OF THE SUM OF 2 NORMAL MATRICES, Linear algebra and its applications, 199, 1994, pp. 329-338
Citations number
8
Categorie Soggetti
Mathematics,Mathematics
Journal title
Linear algebra and its applications → ACNP
ISSN journal
00243795
Volume
199
Year of publication
1994
Pages
329 - 338
Database
ISI
SICI code
0024-3795(1994)199:<329:ABFTDO>2.0.ZU;2-Z
Abstract
We establish an upper bound for the absolute value of the determinant of the Hadamard (elementwise) product of a unitary matrix and a genera l complex matrix. In the case that the general matrix is fixed and the unitary matrix is allowed to vary, this estimate is best possible. As a corollary, we obtain an upper bound for the absolute value of the d eterminant of the sum of two normal matrices with specified eigenvalue s. This corollary supports the determinantal conjecture of Marcus and de Oliveira.