The Inverse Eigenvalue Problem via Orthogonal Matrices

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.

• A. M. Nazari
• B. Sepehrian
• M. Jabari

• Householder matrix
• nonnegative matrix
• Inverse eigenvalue problem.

[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.