On the construction of symmetric nonnegative matrix with prescribed Ritz values

Subject Areas : Linear and multilinear algebra; matrix theory

A. M. Nazaria ^{1 *} , E. Afshari ²

1 - Department of Mathematics, Arak University, P.O. Box 38156-8-8349, Iran
2 - Department of Mathematics, Khomein Branch, Islamic Azad University, Khomein, Iran

Received: 2014-07-25 Accepted : 2014-09-23 Published : 2014-09-25

Keywords: Nonnegative matrix, Ritz values,

Abstract :

In this paper for a given prescribed Ritz values that satisfy in the some specialconditions, we find a symmetric nonnegative matrix, such that the given set be its Ritz values.

References:

[1] Bertram Kostant, Nolan Wallach, GelfandZeitlin theory from the perspective of classical mechanics I, Prog. Math. 243 (2006) 319-364.

 

[2] Bertram Kostant, Nolan Wallach, GelfandZeitlin theory from the perspective of classical mechanics II, Prog. Math. 244 (2006) 387-420.

 

[3] Beresford Parlett, Gilbert Strang, Matrices with prescribed Ritz values, Linear Algebra and its Applications 428 (2008) 1725-1739.

 

[4] A. M. Nazari, F. Sherafat, On the inverse eigenvalue problem for nonnegative matrices of order two to five, Linear Algebra Appl. 436 (2012) 1771-1790.