Results 21 to 30 of about 4,185 (184)
On the relation between Moore's and Penrose's conditions
International Journal of Mathematics and Mathematical Sciences, 2002 Moore (1920) defined the reciprocal of any matrix over the complex field by three conditions, but the beauty of the definition was not realized until Penrose (1955) defined the same inverse using four conditions.
Gaoxiong Gan
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Some results on Drazin-Dagger matrices, reciprocal matrices, and conjugate EP matrices [PDF]
Journal of Mahani Mathematical ResearchIn this paper, a class of matrices, namely, Drazin-dagger matrices, in which the Drazin inverse andthe Moore-Penrose inverse commute, is introduced. Also, some properties of the generalized inverses of these matrices, are investigated.
Mahdiyeh Mortezaei +1 more
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Weighted Moore-Penrose inverse of a boolean matrix
, 1997 If A is a boolean matrix, then the weighted Moore-Penrose inverse of A (with respect to the given matrices M, N) is a matrix G which satisfies AGA = A, GAG = G, and that MAG and GAN are symmetric.
S.K. Jain +5 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, 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.
Yongge Tian
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∗-Regularity in the ring of matrices over the ring of integers modulo 𝑛 [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2023 For any positive integer 𝑛 ≥ 2, we give necessary and sufficient conditions of the existence of the Moore-Penrose inverse of any square matrix over the ring of integers modulo 𝑛.
Wannisa Apairat, Sompong Chuysurichay
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International Journal of Mathematics and Mathematical Sciences, 1992 This paper gives a characterization of EPr-λ-matrices. Necessary and sufficient conditions are determined for (i) the Moore-Penrose inverse of an EPr-λ-matrix to be an EPr-λ-matrix and (ii) Moore-Penrose inverse of the product of EPr-λ-matrices to be an ...
Ar. Meenakshi, N. Anandam
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The generalized Moore-Penrose inverse
, 1991 We define the generalized Moore-Penrose inverse and give necessary and sufficient conditions for its existence over an integral domain. We also prove its uniqueness and give a formula for it which leads us towards a “generalized Cramer's rule” to find ...
Manjunatha Prasad, K. +4 more
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Journal of Mathematics, 2018 Within the framework of the theory of quaternion row-column determinants previously introduced by the author, we derive determinantal representations (analogs of Cramer’s rule) of solutions and Hermitian solutions to the system of two-sided quaternion ...
Ivan I. Kyrchei
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Moore–Penrose inverse of set inclusion matrices
, 2000 Given integers s,k and v, let Wsk be the vs×vk 0–1 matrix, the rows and the columns of which are indexed by the s-subsets and the k-subsets of a v-set respectively, and where the entry in row S and column U is 1 if S⊂U and 0 otherwise.
R.B. Bapat, Bapat, R. B., Bapat, R.B.
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Line digraphs and the Moore-Penrose inverse
, 1981 Various characterizations of line digraphs and of Boolean matrices possessing a Moore-Penrose inverse are used to show that a square Boolean matrix has a Moore-Penrose inverse if and only if it is the adjacency matrix of a line digraph.
Per A. Smeds, Smeds, Per A.
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