Results 11 to 20 of about 2,856 (167)
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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Convexity of the inverse and Moore–Penrose inverse
Linear Algebra and its Applications, 2011 Based on a re-examination of the convexity results for the inverse of positive definite matrices, and the Moore-Penrose inverse of nonnegative definite matrices, a more general concept of strong convexity is defined which provides additional information on the convexity behaviour and geometry of matrix functions known to be strictly convex.
Nordström, Kenneth, Kenneth Nordström
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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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Moore–Penrose inverse in rings with involution
Linear Algebra and its Applications, 2007 Let \(R\) be a ring with involution. An element \(a\in R\) is called regular if there exists an element \(b\in R\) such that \(a=aba\). A regular element \(a \in R\) is called Moore-Penrose invertible if there is an element \(a^\dag \in R\) such that \(aa^\dag a=a\), \(a^\dag aa^\dag=a^\dag\), \((aa^\dag)^*=aa^\dag\) and \((a^\dag a)^*=a^\dag a\).
Koliha, J.J. +2 more
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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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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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A note on the convexity of the Moore–Penrose inverse
Linear Algebra and its Applications, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kenneth, Nordström, Nordström, Kenneth
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Dykstra's Algorithm and a Representation of the Moore–Penrose Inverse
Journal of Approximation Theory, 2002 The convergence of Lardy's series representation of the Moore-Penrose inverse of a closed unbounded linear operator is proved via Dykstra's alternating projection algorithm.
Groetsch, C.W.
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On the covariance of the Moore-Penrose inverse
Linear Algebra and its Applications, 1984 Let A be an \(n\times n\) matrix and T an invertible matrix of the same order. If A is invertible, then, of course, \((TAT^{-1})^{-1}=TA^{- 1}T^{-1}\) and A is covariant under the general linear group. If A is arbitrary and the inverse is replaced by the Moore-Penrose inverse then A is no longer covariant under the full linear group. Given A the author
Robinson, Donald W.
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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