Singular Values,Determinants And Generalized Inverses Of Several Special Matrices

Some kinds of matrices with special structure,such as tridiagonal matrices,pentadiagonal matrices,Toeplitz matrices and Hankel matrices,have not only important theoretic meanings in mathematical fields,such as differential equations,optimization theory,but also play significant roles in some applied fields,such as face recognition,image processing and engineering technology.It has been becoming more and more important to find some crucial parameters,such as eigenvalues,singular values,determinants,inverses and generalized inverses of such matrices.We mainly study the following three parts in this thesis:（1）we compute the singular values of two kinds of 2-Toeplitz type matrices by using the eigenvalues of tridiagonal and pentadiagonal Toeplitz matrices;（2）we compute the determinants of two kinds of pentadiagonal matrices by factorizing a pentadiagonal matrix into the product of two tridiagonal matrices;（3）we study the displacement rank of the W-weighted core-EP inverseA^⊕,W.Estimations for the displacement rank ofA^⊕,^WV-UA^⊕,W are presented.The generalized displacement is also discussed.The general results are applied to the W-weighted core-EP inverse,core-EP inverse and core inverse of a structured matrix such as close-to-Toeplitz matrix and generalized Cauchy matrix.