Results 11 to 20 of about 992,721 (210)
Reverse order law for outer inverses and Moore-Penrose inverse in the context of star order [version 1; peer review: 2 approved] [PDF]
F1000Research, 2022 The reverse order law for outer inverses and the Moore-Penrose inverse is discussed in the context of associative rings. A class of pairs of outer inverses that satisfy reverse order law is determined.
Manjunatha Prasad Karantha +1 more
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Numerical Range of Moore–Penrose Inverse Matrices
Mathematics, 2020 Let A be an n-by-n matrix. The numerical range of A is defined as W ( A ) = { x * A x : x ∈ C n , x * x = 1 } . The Moore–Penrose inverse A + of A is the unique matrix satisfying A A + A = A , A + A A + = A ...
Mao-Ting Chien
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The generalized Moore-Penrose inverse
Linear Algebra and its Applications, 1992 The generalized Moore-Penrose inverse of a matrix over an integral domain with involution is defined. Necessary and sufficient conditions for the existence of this inverse are given. Uniqueness is proven and a formula given which leads toward a ``generalized Cramer's rule'' to find the generalized Moore-Penrose solution.
Manjunatha Prasad, K., Bapat, R.B.
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The Moore-Penrose inverse of a retrocirculant
Linear Algebra and its Applications, 1978 AbstractIn a recent paper Chao [2] has determined the eigenvalues of a matrix of the form A=PC where P is a permutation matrix which commutes with a certain unitary matrix and C is a circulant. Here we determine the Moore-Penrose inverse of such a “retrocirculant” and show that the nonzero eigenvalues of the Moore-Penrose inverse are the reciprocals of
Smith, Ronald L.
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On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product [PDF]
International Journal of Mathematics and Mathematical Sciences, 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.
Yongge Tian
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A characterization of the Moore-Penrose inverse
Linear Algebra and its Applications, 1993 The inverse \(X\) of a square matrix \(A\) may be characterized as the unique matrix for which the two by two block matrix with entries \(\{A,I,I,X\}\) has the same rank as \(A\). This paper gives a generalization for singular and rectangular \(A\) using the Moore-Penrose inverse \(A^ +\).
Fiedler, Miroslav, Markham, Thomas L.
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On the Sequential Composition of the Moore-Penrose Matrix Inverse [PDF]
, 2023 <p>A technical note on the sequential compositionality of the Moore-Penrose Matrix Inverse.
Aziz, Benjamin
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International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract We propose a hierarchical energy management scheme for aggregating Distributed Energy Resources (DERs) for grid flexibility services. To prevent a direct participation of numerous prosumers in the wholesale electricity market, aggregators, as self‐interest agents in our scheme, incentivize prosumers to provide flexibility. We firstly model the
Xiupeng Chen +3 more
wiley +1 more source
On the perturbation of the Moore–Penrose inverse of a matrix [PDF]
Applied Mathematics and Computation, 2020 The Moore-Penrose inverse of a matrix has been extensively investigated and widely applied in many fields over the past decades. One reason for the interest is that the Moore-Penrose inverse can succinctly express some important geometric constructions in finite-dimensional spaces, such as the orthogonal projection onto a subspace and the linear least ...
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A Neural Network for Moore–Penrose Inverse of Time-Varying Complex-Valued Matrices
International Journal of Computational Intelligence Systems, 2020 The Moore–Penrose inverse of a matrix plays a very important role in practical applications. In general, it is not easy to immediately solve the Moore–Penrose inverse of a matrix, especially for solving the Moore–Penrose inverse of a complex-valued ...
Yiyuan Chai +4 more
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