Eventually DSDD Matrices and Eigenvalue Localization

Firstly, the relationships among strictly diagonally dominant ( S D D ) matrices, doubly strictly diagonally dominant ( D S D D ) matrices, eventually S D D matrices and eventually D S D D matrices are considered. Secondly, by excluding some proper subsets of an existing eigenvalue inclusion set for matrices, which do not contain any eigenvalues of matrices, a tighter eigenvalue inclusion set of matrices is derived. As its application, a sufficient condition of determining non-singularity of matrices is obtained. Finally, the infinity norm estimation of the inverse of eventually D S D D matrices is derived