{"title":"The Inverse Eigenvalue Problem via Orthogonal Matrices","authors":"A. M. Nazari, B. Sepehrian, M. Jabari","volume":45,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1241,"pagesEnd":1247,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/14588","abstract":"<p>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.<\/p>\r\n","references":"[1] JONATHAN AXTELL, LIXING HAN, DANIEL HERSHKOWITZ, MICHAEL\r\nNEUMANN, NUNG-SING SZE , Optimition of the spectral radius of a\r\nproduct for nonnegative matrices, Linear Algebra and its Applications\r\n430 (2009) 1442-1451.\r\n[2] J. STOER AND R. BULIRCH, Introduction to numerical analysis, Springer\r\nVerlag 1991.\r\n[3] Fuzhen Zhang. Matrix Theory. Springer-Verlage,1999.\r\n[4] R.Behatia, Matrix Analysis. Springer-Verlage,1973.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 45, 2010"}