Review and classification of recent observers applied in chemical process systems

Core-EP decomposition and its applications

Let R be a ring with involution. In this paper, we introduce a new type of generalized inverse called pseudo core inverse in R. The notion of core inverse was introduced by Baksalary and Tr...

Pseudo core inverses in rings with involution

In this paper, we revise the core EP inverse of a square matrix introduced by Prasad and Mohana in [12], Core EP inverse, Linear and Multilinear Algebra  62 (3) (2014), 792-802. Firstly, we give a new representation and a new characterization of the core EP inverse. Then, we study some properties of the core EP inverse by using a representation by block matrices. Secondly, we extend the notion of core EP inverse to rectangular matrices by means of a weighted core EP decomposition. Finally, we study some properties of weighted core EP inverses. Keywords: Generalized inverses, Moore-Penrose inverse, core inverse, generalized core inverse, core EP inverse, DMP generalized inverse

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Revisiting the core EP inverse and its extension to rectangular matrices

Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains.

On a new generalized inverse for matrices of an arbitrary index

Maximal classes of matrices determining generalized inverses

A geometrical approach on generalized inverses by Neumann-type series

In this paper we introduce a new partial order on a ring, namely the diamond partial order. This order is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, A further algebraic version of Cochran’s theorem and matrix partial orderings, Linear Algebra and its Applications, 127, 157–169, 1990]. We characterize the diamond partial order on rings and study its relationships with other partial orders known in the literature. We also analyse successors, predecessors and maximal elements under the diamond order.

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Néstor Thome

Papers

On a new generalized inverse for matrices of an arbitrary index

Revisiting the core EP inverse and its extension to rectangular matrices

Maximal classes of matrices determining generalized inverses

A geometrical approach on generalized inverses by Neumann-type series

The diamond partial order in rings