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In this paper, we introduce a new generalized inverse, called the G-MPCEP inverse of a complex matrix. We investigate some characterizations, representations, and properties of this new inverse. Cramer's rule for the solution of a singular equation A x = B is also presented. Moreover, the determinantal representations for the G-MPCEP inverse are studied. Finally, the G-MPCEP inverse being used in solving appropriate systems of linear equations is established. [ABSTRACT FROM AUTHOR]

In this paper, we use the well-known Löwner order and the core partial order to introduce a new partial orderon the class of core matrices which is not dominated by any of the known matrix partial orders. We characterize, study its relations with the Löwner partial order under constraints, and exemplify its differences with other partial orders. [ABSTRACT FROM PUBLISHER]

We find expressions for many types of generalized inverses of an arbitrary square complex matrix by using two representations given in [Benítez J. A new decomposition for square matrices. Electron. J. Linear Algebra. 2010;20:207–225] and in [Hartwig RE, Spindelböck K. Matrices for whichandcommute. Linear Multilinear Algebra. 1984;14:241–256]. [ABSTRACT FROM PUBLISHER]

Abstract: The main aim of this paper is to provide a higher-order convergent iterative method in order to calculate the generalized inverse of a given matrix. We extend the iterative method proposed in Li et al. [W.G. Li, Z. Li, A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix, Applied Mathematics and Computation 215 (2010) 3433-3442] to compute the -inverse, generalized inverse -inverse and -inverse. Moreover, we modify the iterative method to compute the generalized inverse of Toeplitz matrices by using the displacement theory. [Copyright &y& Elsevier]

Let T 1 and T 2 be two n × n tripotent matrices and c 1, c 2 two nonzero complex numbers. We mainly study the nonsingularity of combinations T = c 1 T 1 + c 2 T 2 − c 3 T 1 T 2 of two tripotent matrices T 1 and T 2, and give some formulae for the inverse of c 1 T 1 + c 2 T 2 − c 3 T 1 T 2 under some conditions. Some of these results are given in terms of group invertible matrices. [ABSTRACT FROM AUTHOR]

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Abstract: In this note, the outer generalized inverse in Banach algebra is considered, a new representation based on the (1,5) inverse is presented. Also, we construct an iterative method for computing the outer generalized inverse in Banach algebra. [Copyright &y& Elsevier]

Abstract: In this article, we introduce new determinantal representations of the weighted generalized inverse by using a lemma of Robinson [D.W. Robinson, The classical adjoint, Linear Algebra Appl. 411 (2005) 254–276]. And, using generalized Cramer’s rule, we get the method for computing minors of the weighted Moore–Penrose inverse and the W-weighted Drazin inverse. [Copyright &y& Elsevier]

This paper aims to solve the fuzzy Sylvester matrix equation (FSME) A X ˜ + X ˜ B = C ˜ , in which A , B are n × n and m × m crisp matrices, and C ˜ is a n × m fuzzy matrix. Using the Kronecker product, we transform the FSME into an m n × m n fuzzy linear system. Firstly, we obtain the necessary and sufficient conditions for the existence of strong fuzzy solutions to the FSME by using the BT inverse of the coefficient matrix. Secondly, we investigate the existence of a nonnegative BT inverse by using its block structure. Next, we derive general strong fuzzy solutions to a class of FSME and establish an algorithm to obtain general strong fuzzy solutions to the FSME by the BT inverse. Finally, we give three numerical examples and an applied example in the economy to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]