Abstract: By splitting a complex square matrix A=sI-B, where s is an arbitrary complex number, I is the identity matrix and B is a complex square matrix, and by using an existing method of determination of nonsingularity for matrices, some eigenvalue inclusion sets and some methods of determination of nonsingularity for A with two parameters (s and a positive integer k) are obtained and proved to be more accurate and more general than some existing results. Numerical results show that by adjusting s and k, the eigenvalues of A  can be located  more accurate, and  the nonsingularity of A can be determined.

Key words: matrix, eigenvalue, localization, nonsingularity, determination