Results 21 to 30 of about 103 (100)
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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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
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Matrix Analysis for Continuous-Time Markov Chains
Special Matrices, 2021 Continuous-time Markov chains have transition matrices that vary continuously in time. Classical theory of nonnegative matrices, M-matrices and matrix exponentials is used in the literature to study their dynamics, probability distributions and other ...
Le Hung V., Tsatsomeros M. J.
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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
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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
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W-MPD–N-DMP-solutions of constrained quaternion matrix equations
Special Matrices, 2023 The solvability of several new constrained quaternion matrix equations is investigated, and their unique solutions are presented in terms of the weighted MPD inverse and weighted DMP inverse of suitable matrices.
Kyrchei Ivan I. +2 more
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M-matrix and inverse M-matrix extensions
Special Matrices, 2020 A class of matrices that simultaneously generalizes the M-matrices and the inverse M-matrices is brought forward and its properties are reviewed. It is interesting to see how this class bridges the properties of the matrices it generalizes and provides a
McDonald J.J. +6 more
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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
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An algebraic model for the propagation of errors in matrix calculus
Special Matrices, 2020 We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) additive group.
Van Tran Nam, van den Berg Imme
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