Solvability of Inverse Eigenvalue Problem for Dense Singular Symmetric Matrices - Advances in Pure Mathematics

APM > Vol.3 No.1, January 2013

Advances in Pure Mathematics

Volume 3, Issue 1 (January 2013)

ISSN Print: 2160-0368 ISSN Online: 2160-0384

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Solvability of Inverse Eigenvalue Problem for Dense Singular Symmetric Matrices ()

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DOI: 10.4236/apm.2013.31003 3,835 Downloads 6,536 Views Citations

Author(s)

Anthony Y. Aidoo, Kwasi Baah Gyamfi, Joseph Ackora-Prah, Francis T. Oduro

Affiliation(s)

Department of Mathematics and Computer Science, Eastern Connecticut State University, Willimantic, USA.
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.

ABSTRACT

Given a list of real numbers ∧={λ₁,…, λ_n}, we determine the conditions under which ∧will form the spectrum of a dense n × n singular symmetric matrix. Based on a solvability lemma, an algorithm to compute the elements of the matrix is derived for a given list ∧ and dependency parameters. Explicit computations are performed for n≤5 and r≤4 to illustrate the result.

KEYWORDS

Inverse Eigenvalue Problem; Dense; Nonnegative; Singular; Symmetric

Share and Cite:

A. Aidoo, K. Gyamfi, J. Ackora-Prah and F. Oduro, "Solvability of Inverse Eigenvalue Problem for Dense Singular Symmetric Matrices," Advances in Pure Mathematics, Vol. 3 No. 1, 2013, pp. 14-19. doi: 10.4236/apm.2013.31003.

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