Different ZFs lead to different nets: Examples of Zhang generalized inverse

Guo, Dongsheng; Chen, Peng; Jin, Long; Ling, Yingbiao; Zhang, Yunong

doi:10.1109/cac.2013.6775777

Cited by 4 publications

(1 citation statement)

References 12 publications

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“…In [61], starting from theoretical characterizations and representations, the GNN evolution was used in solving underlying matrix equations and proposed a number of algorithms for computing outer and inner inverses with predefined range and/or null space for matrices over a field. In the time-varying case, ZNN evolution is defined using the so-called Zhang functions, which represent the underlying equation in the matrix, vector, or scalar case [31,79].…”

Section: Various Extensions Of a (B C)-inverse And An Inverse Along A...mentioning

confidence: 99%

Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

Ćirić,

Ignjatović,

Stanimirović

2023

Semigroup Forum

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We provide existence criteria and characterizations for outer inverses in a semigroup belonging to the prescribed Green's R-, L -and H -classes. These results generalize the well-known problem of finding outer inverses of a matrix over a field with the prescribed range or/and null space. Outer inverses belonging to the prescribed Green's R-and L -classes also represent extensions of Drazin's (b, c)-inverses and Mary's inverses along an element. We provide an overview of other such extensions that have emerged recently and compare them with the extensions introduced in this paper.

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Section: Various Extensions Of a (B C)-inverse And An Inverse Along A...mentioning

confidence: 99%

Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

Ćirić,

Ignjatović,

Stanimirović

2023

Semigroup Forum

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What is 1/0 in the general sense of physics, applied computation, and/or electronics?

Zhang

Qiu

Ling

et al. 2015

2015 34th Chinese Control Conference (CCC)

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Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

Ćirić

Ignjatović

Stanimirović

2022

Preprint

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We provide existence criteria and characterizations for outer inverses in a semigroup belonging to the prescribed Green’s ℛ-, ℒ- and ℋ-classes. These results generalize the well-known problem of finding outer inverses of a matrix over a field with the prescribed range or/and null space.We show that Mary’s inverse along an element, Drazin’s (b, c)-inverse, and Bott-Duffin (e,f)-inverse of a given element are just three different ways of representing the same notion – the outer inverse of this element belonging to the prescribed Green’s ℋ-class. Hence, outer inverses belonging to the prescribed Green’s ℛ- and ℒ-classes represent extensions of (b,c)-inverses and inverses along an element. We provide an overview of other such extensions that have emerged recently and compare them with the extensions introduced in this paper. Mathematics Subject Classification (2010). 20M99, 15A09, 15A24.

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Different ZFs lead to different nets: Examples of Zhang generalized inverse

Cited by 4 publications

References 12 publications

Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

What is 1/0 in the general sense of physics, applied computation, and/or electronics?

Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

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