The Inverse Eigenvalue Problem via Orthogonal Matrices

Authors: A. M. Nazari, B. Sepehrian, M. Jabari

Abstract:

In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.

Keywords: Householder matrix, nonnegative matrix, Inverse eigenvalue problem.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335124

References:

[1] JONATHAN AXTELL, LIXING HAN, DANIEL HERSHKOWITZ, MICHAEL NEUMANN, NUNG-SING SZE , Optimition of the spectral radius of a product for nonnegative matrices, Linear Algebra and its Applications 430 (2009) 1442-1451.
[2] J. STOER AND R. BULIRCH, Introduction to numerical analysis, Springer Verlag 1991.
[3] Fuzhen Zhang. Matrix Theory. Springer-Verlage,1999.
[4] R.Behatia, Matrix Analysis. Springer-Verlage,1973.