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초록· 키워드
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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.
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참고문헌 (5)
참고문헌 신청
A. Leal Duarte / 2002 / On the minimum number of distinct eigenvalues for a symmetric matrix whose graph is a given tree / Math. Inequal. Appl 5 (2) : 175 ~ 180
C. Godsil / 2001 / Algebraic graph theory, Graduate Texts in Mathematics / Springer-Verlag : 207 ~
C. R. Johnson / 1999 / The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree / Linear and Multilinear Algebra 46 (1) : 138 ~ 144
C. R. Johnson / 2003 / The Parter-Wiener theorem: refine-ment and generalization / SIAM J. Matrix Anal. Appl 25 (2) : 352 ~ 361
R. Horn / 1985 / Matrix analysis / Cambridge University Press
C. Godsil / 2001 / Algebraic graph theory, Graduate Texts in Mathematics / Springer-Verlag : 207 ~
C. R. Johnson / 1999 / The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree / Linear and Multilinear Algebra 46 (1) : 138 ~ 144
C. R. Johnson / 2003 / The Parter-Wiener theorem: refine-ment and generalization / SIAM J. Matrix Anal. Appl 25 (2) : 352 ~ 361
R. Horn / 1985 / Matrix analysis / Cambridge University Press
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