Construct a matrix with prescribed Ritz values of the order less than or equal to three

Document Type : Original Paper


Department of Mathematics, Arak University, Arak, Iran


The Ritz values of a matrix are the set of all the eigenvalues of the leading principal submatrices. In this paper, assuming that the set of Ritz values is given from the dimension of maximum three, we find a matrix such that the given set is its Ritz values. The conditions for the existing solution are also studied.


Main Subjects

[1] م. نیکوکار و م. درویشی، محاسبات عددی، انتشارات گسترش علوم پایه، چاپ سی و پنجم ، (1389).
[2]  ع.م. نظری و ع. نظامی، تاریخچه مسئله مقدار ویژه معکوس ماتریس های نامنفی، مجله فرهنگ و اندیشه ریاضی، سال سی و نهم، شماره 2 (پیاپی 67، پاییز و زمستان 1399).
[3] A. M. Nazari, E. Afshari, On the construction of symmetric nonnegative matrix with prescribed Ritz values, Journal of Linear and Topological Algebra, Vol. 03, No. 02, 2014, 61- 66.
[4] B. Parlett a, G. Strang, Matrices with prescribed Ritz values, Linear Algebra and its Applications 428 (2008) 1725–1739.
Volume 12, Issue 4 - Serial Number 28
January 2022
Pages 548-556
  • Receive Date: 16 March 2022
  • Revise Date: 30 September 2022
  • Accept Date: 13 December 2022
  • First Publish Date: 22 December 2022