Abstract
The concept of star-dagger matrices was introduced in 1984 by Hartwig and Spindelböck. While they completely characterized the star-dagger matrices by using a block decomposition of the form PQ00 , they also proposed the following open problem: “Can the triangular form PQ0Rbe used to obtain further results on the star-dagger matrices?” In this paper, we have attempted this open problem by using an upper-triangularization of Schur’s type for a square matrix, namely, the core-EP decomposition. Furthermore, similar problems regarding bi-dagger and bi-EP matrices are investigated.
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