A Note on Inclusion Intervals of Matrix Singular Values

The set of all n-by-n complex matrices is denoted by Cn×n. Let A aij ∈ Cn×n. Denote the Hermitian adjoint of matrix A by A∗. Then the singular values of A are the eigenvalues of AA∗ . It is well known that matrix singular values play a very key role in theory and practice. The location of singular values is very important in numerical analysis and many other applied fields. For more review about singular values, readers may refer to 1–9 and the references therein. Let N {1, 2, . . . , n}. For a given matrix A aij ∈ Cn×n, we denote the deleted absolute row sums and column sums of A by