Results 21 to 30 of about 672 (66)
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
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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On the Relative Gain Array (RGA) with Singular and Rectangular Matrices
, 2019 In this paper we identify a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices.
Uhlmann, Jeffrey
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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
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.
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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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The Nullity Theorem for Principal Pivot Transform
, 2013 We generalize the nullity theorem of Gustafson [Linear Algebra Appl. (1984)] from matrix inversion to principal pivot transform. Several special cases of the obtained result are known in the literature, such as a result concerning local complementation ...
Brijder, Robert
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Open Mathematics, 2018 In this paper, we introduce the weak group inverse (called as the WG inverse in the present paper) for square complex matrices of an arbitrary index, and give some of its characterizations and properties.
Wang Hongxing, Chen Jianlong
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, 2000 Abstract and Applied Analysis, Volume 5, Issue 3, Page 137-146, 2000.
Anatolij I. Perov
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