Core inverse of matrices

By O. Baksalary, G. Trenkler. 2010

461 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a2dd3c08def88d31e36499fe6e8e57e8c405f90e

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In Atomic and Molecular Physics, and Optics

In Computational Theory and Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

On a new generalized inverse of matrices (2018, background): “In 2010, Baksalary and Trenkler in [4] introduced core inverse of a matrix A ∈ Cn×n of index at most one as the unique matrix A such that AA = PA, the orthogonal projector onto C(A), and C(A ) ⊆ C(A).”
Characterizations and Representations of Core and Dual Core Inverses (2016, background): “he symbols a{1,3} and a{1,4} denote the sets of all {1,3}-inverses and {1,4}-inverses of a, respectively. The concept of core inverse of a complex matrix was ﬁrst introduced by Baksalary and Trenkler [2]. Recently, Raki´c et al. [9] generalized the deﬁnition of core inverse to the ring case. An elem”
ON ONE-SIDED (B;C)-INVERSES OF ARBITRARY MATRICES (2017, background): “Given A ∈ Cn such that A is group invertible, according to [1] and [19], AA © and A# ©A are orthogonal projectors.”
Group, Moore–Penrose, core and dual core inverse in rings with involution☆ (2014, background): “2, we can generalize results from [1] and obtain a large number of new characterizations of EP-ness of a.”
Pseudo core inverses in rings with involution (2016, background): “The notion of core inverse was introduced by Baksalary and Trenkler for matrices of index 1 in 2010 and then it was generalized to an arbitrary ∗-ring case by Rakić, Dinčić and Djordjević in 2014.”
Weighted core–EP inverse of an operator between Hilbert spaces (2019, background): “The core inverse of A exists if and only if ind(A) ≤ 1 [12,13].”
Characterizations of k-commutative equalities for some outer generalized inverses (2018, methodology): “The core inverse was introduced by Baksalary and Trenkler in [1].”
The DMP inverse for rectangular matrices (2017, background): “We refer the readers to [1, 2, 11] for basic results on these generalized inverses.”
New characterizations for core inverses in rings with involution (2015, unknown): “R A ] 2 6 D ec 2 01 5 New characterizations for core inverses in rings with involution Sanzhang Xu∗, Jianlong Chen†, Xiaoxiang Zhang‡ Department of Mathematics, Southeast University Nanjing 210096, China The core inverse for a complex matrix was introduced by Baksalary and Trenkler.”
Core–EP inverse (2014, methodology): “Baksalary–Trenkler in [2] noted that the core inverse defined by them coincides with Bott–Duffin inverse PA[(A − I )PA + I ]−1, where PA is the orthogonal projection onto the column space of A.”
Characterizations of core and dual core inverses in rings with involution (2016, unknown): “The core and dual core inverse of a complex matrix were introduced by Baksalary and Trenkler [3].”
Weak group inverse (2017, background): “ is called the group inverse of A, and is denoted as X = A# (see [3]). The core inverse of A ∈ CCM n is deﬁned as the unique matrix X ∈ C n,n satisfying AX = AA†, R(X) ⊆ R(A) and is denoted as X = A# [1]. When A ∈ CCM n , we call it a core invertible (or group invertible) matrix. Recently, the resea”
Characterizations of the core inverse and the core partial ordering (2015, background): “Linear and Multilinear Algebra, 2015 Vol. 63, No. 9, 1829–1836, http://dx.doi.org/10.1080/03081087.2014.975702 Characterizations of the core inverse and the core partial ordering Hongxing Wanga∗ and Xiaoji Liub aDepartment of Mathematics, Huainan Normal University, Anhui, P.R. China; bCollege of Mat”