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Solvability of Inverse Eigenvalue Problem for Dense Singular Symmetric Matrices
Department of Mathematics and Computer Science, Eastern Connecticut State University, Willimantic, USA
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
- 1 Department of Mathematics and Computer Science, Eastern Connecticut State University, Willimantic, USA
- 2 Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
- 3 Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
- 4 Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Advances in Pure Mathematics·Volume 03 (2013)·Pages 14–19·Published 11 January 2013·DOI10.4236/apm.2013.31003
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Abstract
Given a list of real numbers ∧ ={ λ 1 , … , 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.
KeywordsInverse Eigenvalue ProblemDenseNonnegativeSingularSymmetric
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