부산대학교 도서관

This article deals with establishing new properties of star-dagger, bi-normal, bi-dagger and bi-EP matrices using the core-EP decomposition of Wang: for any square complex matrix $A$ of index $k=ind(A)$, there is a unitary matrix $U$ of the same size such that $A=U \left[\smallmatrix T & S \\ 0 & N \endsmallmatrix\right] U^{*}$ where $T$ is a nonsingular upper-triangular square matrix and $N$ is a square nilpotent matrix with $ind(N)=k$. \par Some of the results include core-EP decomposition of natural powers of $A$, the equivalence of $A^m$ and $N^m$ being partial isometries, equivalent conditions of $A$ and $A^2$ being star-dagger, and equivalent conditions of $A$ being bi-EP or bi-dagger. \par The results are illustrated using examples.