Further Results on Weighted Core-EP Inverse of Matrices
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Results in Mathematics
Further Results on Weighted Core-EP Inverse of Matrices Ratikanta Behera , Gayatri Maharana, and Jajati Keshari Sahoo Abstract. In this paper, we introduce the notation of E-weighted core-EP and F -weighted dual core-EP inverse of matrices. We then obtain a few explicit expressions for the weighted core-EP inverse of matrices through other generalized inverses. Further, we discuss the existence of generalized weighted Moore–Penrose inverse and additive properties of the weighted core-EP inverse of matrices. In addition to these, we propose the star weighted core-EP and weighted core-EP star class of matrices for solving the system of matrix equations. We further elaborate on this theory by producing a few representation and characterization of star weighted coreEP and weighted core-EP star classes of matrices. AMS Subject Classifications. 15A09, 15A24, 15A30. Keywords. Weighted core-EP inverse, weighted dual core-EP inverse, additive properties, outer inverse, generalized Moore–Penrose inverse.
1. Introduction The core and core-EP inverses of matrices have been intensively studied in recent years to solve a certain type of matrix equations [1,2]. Hence, a significant number of papers explored the characterizations of the core inverse and its applications in [3,12,13,25]. A few properties of the core inverse and interconnections with different generalized inverses were discussed in [1,12,21,26]. The core-EP inverse of matrices, introduced by Prasad and Mohana [16], have significantly impacted for square matrices. Then several characterizations of the core-EP inverse and its extension to rectangular matrices were discussed in [9]. 0123456789().: V,-vol
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In this connection, the authors of [10] have discussed the weighted core-EP inverse and several representations in terms of matrix decomposition. Further, a few characterizations and properties of the core-EP inverse with other inverses are discussed in [11,16,22,24]. The last literature on core-EP, weighted coreEP inverses of matrices along with its multifarious extensions [14,15,17,27], motivate us to study and introduce E-weighted core-EP and F -weighted dual core-EP inverse of matrices. We mention below a summary of the main points of the discussion. • The notations of E-weighted core-EP and F -weighted dual core-EP inverses are proposed. Through these definitions, the existence of generalized weighted Moore–Penrose inverse is discussed. • Introduce several explicit expression for the weighted core-EP inverse of matrices through other generalized inverses, like, Drazin inverses, weighted core inverse, and generalized Moore–Penrose inverses. • We have discussed additive properties of the E-weighted core-EP and F -weighted dual core-EP inverse of matrices. • Introduce star weighted core-EP and weighted core-EP star matrices to solve the system of matrix equations. • A few characterization and representation of star weighted core-EP and weighted core-EP star classes of matrices are discussed. Th
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