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By applying the properties of Schur complement and some inequality techniques, some new estimates of diagonally dominant degree on the Schur complement of matrices are obtained, which improve the main results of Liu (SIAM J. Matrix Anal. Appl. 27:665-674, 2005) and Liu (Linear Algebra Appl. 432:1090-1104, 2010). As an application, we present some new distribution theorems for eigenvalues of the Schur complement. Finally, we give a numerical example to illustrate the theory results.

The estimates of diagonally dominant degree and eigenvalues distributions for the Schur complements of matrices