A family of 512 reverse order laws for generalized inverses of a matrix product: A review [PDF]
Heliyon, 2020 Reverse order laws for generalized inverses of matrix products are a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product AB is (AB)(i,…,j)=B(s2,…,t2)A(s1,…,t1), where (⋅)(i,…,j ...
Yongge Tian
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Weak dual generalized inverse of a dual matrix and its applications [PDF]
Heliyon, 2023 Recently, the dual Moore-Penrose generalized inverse has been applied to study the linear dual equation when the dual Moore-Penrose generalized inverse of the coefficient matrix of the linear dual equation exists.
Hong Li, Hongxing Wang
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Secondary range symmetric matrices [version 2; peer review: 2 approved, 1 approved with reservations] [PDF]
F1000ResearchThe concept of secondary range symmetric matrices is introduced here. Some characterizations as well as the equivalent conditions for a range symmetric matrix to be secondary range symmetric matrix is given.
Divya Shenoy
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Hybrid Sensor Placement Framework Using Criterion-Guided Candidate Selection and Optimization [PDF]
SensorsThis study presents a hybrid sensor placement methodology that combines criterion-based candidate selection with advanced optimization algorithms. Four established selection criteria—modal kinetic energy (MKE), modal strain energy (MSE), modal assurance ...
Se-Hee Kim +3 more
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The Geometry of Generalized Inverses
Journal of the Royal Statistical Society Series B: Statistical Methodology, 1975 Summary Generalized inverses of linear transformations must satisfy at least the natural requirement that they are true inverses for appropriately restricted subspaces. There are three other characteristics that may or may not hold independently.
William Kruskal
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Reverse order law for outer inverses and Moore-Penrose inverse in the context of star order [version 1; peer review: 2 approved] [PDF]
F1000Research, 2022 The reverse order law for outer inverses and the Moore-Penrose inverse is discussed in the context of associative rings. A class of pairs of outer inverses that satisfy reverse order law is determined.
Manjunatha Prasad Karantha +1 more
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Characterizations of Matrix Equalities for Generalized Inverses of Matrix Products
Axioms, 2022 This paper considers how to construct and describe matrix equalities that are composed of algebraic operations of matrices and their generalized inverses.
Yongge Tian
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Invariance property of a five matrix product involving two generalized inverses
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Matrix expressions composed by generalized inverses can generally be written as f(A−1, A−2, . . ., A−k), where A1, A2, . . ., Ak are a family of given matrices of appropriate sizes, and (·)− denotes a generalized inverse of matrix.
Jiang Bo, Tian Yongge
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Generalized inverses in graph theory
AKCE International Journal of Graphs and Combinatorics, 2023 –In this article, some interesting applications of generalized inverses in the graph theory are revisited. Interesting properties of generalized inverses are employed to make the proof of several known results simpler, and several techniques such as ...
Umashankara Kelathaya +2 more
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Characterizations of the group invertibility of a matrix revisited
Demonstratio Mathematica, 2022 A square complex matrix AA is said to be group invertible if there exists a matrix XX such that AXA=AAXA=A, XAX=XXAX=X, and AX=XAAX=XA hold, and such a matrix XX is called the group inverse of AA.
Tian Yongge
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