论文信息 - The trees for which maximum multiplicity implies the simplicity of other eigenvalues

The trees for which maximum multiplicity implies the simplicity of other eigenvalues

Among those real symmetric matrices whose graph is a given tree T, the maximum multiplicity is known to be the path cover number of T. An explicit characterization is given for those trees for which whenever the maximum multiplicity is attained, all other multiplicities are 1.

Charles R. Johnson | Carlos M. Saiago

[1] S. Parter. On the Eigenvalues and Eigenvectors of a Class of Matrices , 1960 .

[2] Gerry Wiener. Spectral multiplicity and splitting results for a class of qualitative matrices , 1984 .

[3] Charles R. Johnson,et al. The Parter-Wiener Theorem: Refinement and Generalization , 2003, SIAM J. Matrix Anal. Appl..

[4] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5] Charles R. Johnson,et al. The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree , 1999 .

[6] Charles R. Johnson,et al. On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph , 2003 .

[7] Charles R. Johnson,et al. Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix , 2002 .