1D inverse and D1 inverse of square matrices

Sahoo, Jajati Keshari and Maharana, Gayatri and Sitha, Bibekananda and Thome, Nestor (2024) 1D inverse and D1 inverse of square matrices. Miskolc Mathematical Notes, 25 (1). pp. 445-463. ISSN 1787-2413

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Abstract

In this paper we introduce two new classes of inverses for square matrices, which are called 1Drazin (in short, 1D) inverse and Drazin1 (in short, D1) inverse. Next, we investigated the existence and uniqueness of 1D inverse and its dual D1 inverse. Some representation and characterizations of these inverses are derived. In addition to this, we obtain some properties of 1D and D1 inverses through idempotent and binary relations.

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