Paper's Title:

A Determinantal Representation of Core EP Inverse

Author(s):

Divya Shenoy Purushothama

Department of Mathematics,
Manipal Institute of Technology,
Manipal Academy of Higher Education,
Manipal -576104, Karnataka,
India.
E-mail:  divya.shenoy@manipal.edu
URL: https://manipal.edu/mit/department-faculty/faculty-list/divya-shenoy-p.html

Abstract:

The notion of Core EP inverse is introduced by Prasad in the article "Core - EP inverse" and proved its existence and uniqueness. Also, a formula for computing the Core EP inverse is obtained from particular linear combination of minors of a given matrix. Here a determinantal representation for Core EP inverse of a matrix A with the help of rank factorization of A is obtained.

Paper's Title:

The Drazin-star and Star-Drazin Solutions to Quaternion Matrix Equations

Author(s):

Ivan I. Kyrchei, Dijana Mosić, Predrag Stanimirović

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
of NAS of Ukraine, L'viv, 79060,
Ukraine.
E-mail: ivankyrchei26@gmail.com

Faculty of Sciences and Mathematics, University of Niš, P.O.
Box 224, 18000, Niš, Serbia.
E-mail: dijana@pmf.ni.ac.rs

Faculty of Sciences and Mathematics, University of Niš, P.O.
Box 224, 18000, Niš, Serbia.
E-mail: pecko@pmf.ni.ac.rs

Abstract:

The notions of the Drazin-star and star-Drazin matrices are expanded to quaternion matrices in this paper. Their determinantal representations are developed in both cases in terms of noncommutative row-column determinants of quaternion matrices and for minors of appropriate complex matrices. We study all possible two-sided quaternion matrix equations with their one-sided partial cases whose uniquely determined solutions are based on the Drazin-star and star-Drazin matrices. Solutions of these equations are represented by Cramer's rules in both cases for quaternion and complex matrix equations. A numerical example is presented to illustrate our results.

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