Results 11 to 20 of about 671 (66)
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
wiley +1 more source
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
doaj +1 more source
On the relation between Moore′s and Penrose′s conditions
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 8, Page 505-509, 2002., 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. The reciprocal is now often called the Moore-Penrose inverse, and has been widely used in various areas.
Gaoxiong Gan
wiley +1 more source
A note on computing the generalized inverse A T,S (2) of a matrix A
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 8, Page 497-507, 2002., 2002 The generalized inverse A T,S (2) of a matrix A is a {2}‐inverse of A with the prescribed range T and null space S. A representation for the generalized inverse A T,S (2) has been recently developed with the condition σ (GA| T) ⊂ (0, ∞), where G is a matrix with R(G) = T andN(G) = S. In this note, we remove the above condition. Three types of iterative
Xiezhang Li, Yimin Wei
wiley +1 more source
On decompositions of estimators under a general linear model with partial parameter restrictions
Open Mathematics, 2017 A general linear model can be given in certain multiple partitioned forms, and there exist submodels associated with the given full model. In this situation, we can make statistical inferences from the full model and submodels, respectively.
Jiang Bo, Tian Yongge, Zhang Xuan
doaj +1 more source
Miscellaneous equalities for idempotent matrices with applications
Open Mathematics, 2020 This article brings together miscellaneous formulas and facts on matrix expressions that are composed by idempotent matrices in one place with cogent introduction and references for further study.
Tian Yongge
doaj +1 more source
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.
doaj +1 more source
On matrix convexity of the Moore‐Penrose inverse
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 707-710, 1996., 1995 Matrix convexity of the Moore‐Penrose inverse was considered in the recent literature. Here we give some converse inequalities as well as further generalizations.
B. Mond, J. E. Pečarić
wiley +1 more source
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
doaj +1 more source
A novel interpretation of least squares solution
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 1, Page 41-46, 1992., 1991 We show that the well‐known least squares (LS) solution of an overdetermined system of linear equations is a convex combination of all the non‐trivial solutions weighed by the squares of the corresponding denominator determinants of the Cramer′s rule. This Least Squares Decomposition (LSD) gives an alternate statistical interpretation of least squares,
Jack-Kang Chan
wiley +1 more source