New matrix partial order based on spectrally orthogonal matrix decomposition

Abstract

We investigate partial orders on the set of complex square matrices and introduce a new order relation based on spectrally orthogonal matrix decompositions. We also establish the relation of this concept with the known orders.

Pseudo core invertibility and DMP invertibility in two semigroups of a ring with involution

“…For more details of pseudo core inverses and DMP inverses, for example, see [18,28]. Noted that some generalized inverse matrices can provide a method to define pre-orders or partial orders and to analyze binary relations, for example, see [3,9,11,12,15]. Except that, many scholars have studied projections related to generalized inverses and their generalizations, such as [4,14,25].…”

Determinantal Representations of the Core Inverse and Its Generalizations with Applications

“…Other generalizations of the core inverse were recently introduced for n × n complex matrices, namely, BT inverses [5], DMP inverses [6], CMP inverses [7], etc. e characterizations, computing methods, some applications of the core inverse, and its generalizations were recently investigated in complex matrices and rings (see, e.g., [3,[8][9][10][11][12][13][14][15][16][17][18]).…”

Órdenes parciales y pre-órdenes definidos a partir de matrices inversas generalizadas.

“…El pre-orden de Drazin se obtuvo al intentar utilizar la misma idea con la inversa de Drazin [48]. En [1,3,4,7,8,9,11,20,21,23,24,25,38,41,45,48,50] N. Castro-González y J. Vélez-Cerrada consideraron, en [16], el concepto…”