논문KCI 등재
Classification of trees each of whose associated acyclic matrices with distinct diagonal entries has distinct eigenvalues
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It is known that each eigenvalue of a real symmetric, irre-ducible, tridiagonal matrix has multiplicity 1. The graph of such a matrixis a path. In this paper, we extend the result by classifying those treesfor which each of the associated acyclic matrices has distinct eigenvalueswhenever the diagonal entries are distinct.
Abstract
It is known that each eigenvalue of a real symmetric, irre-ducible, tridiagonal matrix has multiplicity 1. The graph of such a matrixis a path. In this paper, we extend the result by classifying those treesfor which each of the associated acyclic matrices has distinct eigenvalueswhenever the diagonal entries are distinct.
참고문헌 (5)
- A. Leal Duarte, "On the minimum number of distinct eigenvalues for a symmetric matrix whose graph is a given tree", Math. Inequal. Appl, 5(2), pp.175~180 (2002)
- C. Godsil, "Algebraic graph theory, Graduate Texts in Mathematics", pp.207~ (2001), Springer-Verlag
- R. Horn, "Matrix analysis" (1985), Cambridge University Press
- C. R. Johnson, "The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree", Linear and Multilinear Algebra, 46(1), pp.138~144 (1999)
- C. R. Johnson, "The Parter-Wiener theorem: refine-ment and generalization", SIAM J. Matrix Anal. Appl, 25(2), pp.352~361 (2003)
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