Results 21 to 30 of about 772 (64)
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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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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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
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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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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
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Idempotent operator and its applications in Schur complements on Hilbert C*-module
Special Matrices, 2023 The present study proves that TT is an idempotent operator if and only if R(I−T∗)⊕R(T)=X{\mathcal{ {\mathcal R} }}\left(I-{T}^{\ast })\oplus {\mathcal{ {\mathcal R} }}\left(T)={\mathcal{X}} and (T∗T)†=(T†)2T{\left({T}^{\ast }T)}^{\dagger }={\left({T ...
Karizaki Mehdi Mohammadzadeh +1 more
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International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 2, Page 261-266, 1992., 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 EPr‐λ‐matrix.
Ar. Meenakshi, N. Anandam
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Generalized two point boundary value problems. existence and uniqueness
International Journal of Stochastic Analysis, Volume 5, Issue 2, Page 147-156, 1992., 1991 An algorithm is presented for finding the pseudo‐inverse of a rectangular matrix. Using this algorithm as a tool, existence and uniqueness of solutions to two point boundary value problems associated with general first order matrix differential equations are established.
K. N. Murty, S. Sivasundaram
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Bordering method to compute Core-EP inverse
Special Matrices, 2018 Following the work of Kentaro Nomakuchi[10] and Manjunatha Prasad et.al., [7] which relate various generalized inverses of a given matrix with suitable bordering,we describe the explicit bordering required to obtain core-EP inverse, core-EP generalized ...
Prasad K. Manjunatha, Raj M. David
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Closed-form formula for a classical system of matrix equations
Arab Journal of Basic and Applied Sciences, 2022 Keeping in view the latest development of anti-Hermitian matrix in mind, we construct some closed form formula for a classical system of matrix equations having anti-Hermitian nature in this paper.
Abdur Rehman +4 more
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