Commenced in January 2007
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Paper Count: 2

Search results for: nonnegative matrix

2 Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Authors: Jing Li, Guang Zhou

Abstract:

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.

Keywords: hadamard product, M-matrix, spectral radius, Fan product; nonnegative matrix, Minimum eigenvalue

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1 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

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