Results 81 to 90 of about 23,672 (221)

Efficient GMM estimation with singular system of moment conditions

Statistical Theory and Related Fields, 2020
Standard generalised method of moments (GMM) estimation was developed for nonsingular system of moment conditions. However, many important economic models are characterised by singular system of moment conditions.
Zhiguo Xiao
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Condition numbers for the Moore-Penrose inverse and the least squares problem involving rank-structured matrices [PDF]

, 2023
Sk. Safique Ahmad, Pinki Khatun
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Singular matrices possessing the triangle property

Special Matrices
It is known that the inverse of an invertible real square matrix satisfying the triangle property is a tridiagonal matrix. In this note, results that may be considered as analogues of this assertion are obtained for the Moore-Penrose inverse and the ...
Priya K. Kranthi, Sivakumar K. C.
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Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse

Journal of Applied Mathematics, 2014
This paper presents a computational iterative method to find approximate inverses for the inverse of matrices. Analysis of convergence reveals that the method reaches ninth-order convergence.
F. Soleymani, M. Sharifi, S. Shateyi
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Moore–Penrose inverse of set inclusion matrices

Linear Algebra and its Applications, 2000
The set inclusion matrix \(W_{sk}\) with dimensions \(\binom vs\times\binom vk\), where \(s\), \(k\) and \(v\) are integers satisfying \(0\leq s\leq k\leq v\), is defined as follows. The rows and columns of \(W_{sk}\) are indexed by the \(s\)-element subsets and by the \(k\)-element subsets of a \(v\)-element set, respectively, and the entry in row \(S\
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Minors of the Moore-Penrose inverse

Linear Algebra and its Applications, 1993
The well-known Jacobi identity for the minors of an inverse matrix \(A^{-1}\) is generalized to the minors of the Moore-Penrose inverse \(A^ +\) of an arbitrary real \(m \times n\)-matrix \(A\) of rank \(r \geq 1\). As a consequence, conditions are given in the case \(m=n\), under which all principal minors of \(A^ +\) are nonnegative.
Miao, Jianming, Ben-Israel, Adi
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Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space

The Scientific World Journal, 2013
We introduce some new algebraic and topological properties of the Minkowski inverse A⊕ of an arbitrary matrix A∈Mm,n (including singular and rectangular) in a Minkowski space μ.
Hanifa Zekraoui, Zeyad Al-Zhour, Cenap Özel   +2 more
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The Moore–Penrose inverse of a factorization

Linear Algebra and its Applications, 2003
Let \(A\) be a von Neumann regular matrix (i.e., \(AXA= A\) is solvable), and let \(P\), \(Q\) be given. Assume that there exist \(P'\) and \(Q'\) such that \(P'PA= A= AQQ'\). Necessary and sufficient conditions are given in order to \(PAQ\) be Moore-Penrose invertible, generalizing previous results.
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Moore-Penrose Inverse and Semilinear Equations

Advances in Linear Algebra & Matrix Theory, 2018
In this paper, we study the existence of solutions for the semilinear equation , where A is a , , and is a nonlinear continuous function. Assuming that the Moore-Penrose inverse AT(AAT)-1 exists (A denotes the transposed matrix of A) which is true whenever the determinant of the matrix AAT is different than zero, and the following condition on the ...
Hugo Leiva, Raúl Manzanilla
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Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation AXB+CXD=E with the Least Norm

Journal of Applied Mathematics, 2014
Using the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the
Shi-Fang Yuan
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