Results 1 to 10 of about 99 (97)
The dual index and dual core generalized inverse
Open Mathematics, 2023 In this article, we introduce the dual index and dual core generalized inverse (DCGI). By applying rank equation, generalized inverse, and matrix decomposition, we give several characterizations of the dual index when it is equal to 1. We realize that if
Wang Hongxing, Gao Ju
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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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Displacement structure of the DMP inverse
Open Mathematics, 2022 A matrix AA is said to have the displacement structure if the rank of the Sylvester displacement AU−VAAU-VA or the Stein displacement A−VAUA-VAU is much smaller than the rank of AA.
Zhong Jin, Yang Hong
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The group inverse of circulant matrices depending on four parameters
Special Matrices, 2021 Explicit expressions for the coefficients of the group inverse of a circulant matrix depending on four complex parameters are analytically derived. The computation of the entries of the group inverse are now reduced to the evaluation of a polynomial ...
Carmona A. +3 more
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The 𝔪-WG° inverse in the Minkowski space
Open Mathematics, 2023 In this article, we study the m{\mathfrak{m}}-WG∘{}^{\circ } inverse which presents a generalization of the m{\mathfrak{m}}-WG inverse in the Minkowski space. We first show the existence and the uniqueness of the generalized inverse.
Liu Xiaoji, Zhang Kaiyue, Jin Hongwei
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A combinatorial expression for the group inverse of symmetric M-matrices
Special Matrices, 2021 By using combinatorial techniques, we obtain an extension of the matrix-tree theorem for general symmetric M-matrices with no restrictions, this means that we do not have to assume the diagonally dominance hypothesis.
Carmona A., Encinas A.M., Mitjana M.
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Matrix rank and inertia formulas in the analysis of general linear models
Open Mathematics, 2017 Matrix mathematics provides a powerful tool set for addressing statistical problems, in particular, the theory of matrix ranks and inertias has been developed as effective methodology of simplifying various complicated matrix expressions, and ...
Tian Yongge
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Diagonal dominance and invertibility of matrices
Special Matrices, 2023 A weakly diagonally dominant matrix may or may not be invertible. We characterize, in terms of combinatorial structure and sign pattern when such a matrix is invertible, which is the common case. Examples are given.
Johnson Charles Royal +2 more
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On mixed‐type reverse‐order laws for the Moore‐Penrose inverse of a matrix product
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 58, Page 3103-3116, 2004., 2004 Some mixed‐type reverse‐order laws for the Moore‐Penrose inverse of a matrix product are established. Necessary and sufficient conditions for these laws to hold are found by the matrix rank method. Some applications and extensions of these reverse‐order laws to the weighted Moore‐Penrose inverse are also given.
Yongge Tian
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Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix
Special Matrices, 2021 In this paper, we consider a new Sylvester-Kac matrix, i.e., Fibonacci-Sylvester-Kac matrix. We discuss the eigenvalues, eigenvectors and characteristic polynomial of this matrix in two categories based on whether the Fibonacci-Sylvester-Kac matrix order
Jiang Zhaolin, Zheng Yanpeng, Li Tianzi
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