Abstract:

Cauchy interlacing theorem is a well-known theory in matrix theory, which can be used to reveal the close relationship between the multiplicity of eigenvalues of real symmetric matrix and the multiplicity of eigenvalues of its principal submatrix. The concepts of P-vertex and P-set of real symmetric matrices are proposed based on the multiplicity of eigenvalues of matrices and Cauchy's Interlacing Theorem. This talk will introduce some combinatorial properties of P-vertex and P-set of real symmetric matrices.