Reverse order law for the Moore–Penrose inverse

Djordjević, Dragan S.; Dinčić, Nebojša Č.

doi:10.1016/j.jmaa.2009.08.056

Cited by 63 publications

(34 citation statements)

References 12 publications

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“…In this paper, we present a purely algebraic proof of some equivalent conditions related to the reverse order law for the Moore-Penrose inverse in C * -algebras, extending the known results for matrices [15,16] and Hilbert space operators [4,5]. We show that neither the rank (in the finite dimensional case) nor the properties of operator matrices (in the infinite dimensional case) are necessary for the proof of the reverse order rule for the Moore-Penrose inverse valid under certain conditions on regular elements.…”

Section: Mosić and Ds Djordjevićmentioning

confidence: 80%

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Reverse order law for the Moore-Penrose inverse in C*-algebras

Mosić¹,

Djordjević²

2011

ELA

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Section: Mosić and Ds Djordjevićmentioning

confidence: 80%

“…The operator analogues of these results for the MoorePenrose inverse are proved in [4,5] for linear bounded operators on Hilbert spaces, using the matrix form of operators induced by some natural decomposition of Hilbert spaces.…”

Section: Mosić and Ds Djordjevićmentioning

confidence: 96%

Reverse order law for the Moore-Penrose inverse in C*-algebras

Mosić¹,

Djordjević²

2011

ELA

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“…Related results can be found in [5,14,15]. Next theorem describes the form of both matrices A and B for which the Moore-Penrose inverse satisfies that property.…”

Section: A Simultaneous Canonical Form Of a Pair Of Matricesmentioning

confidence: 86%

A simultaneous canonical form of a pair of matrices and applications involving the weighted Moore–Penrose inverse

Thome

2016

Applied Mathematics Letters

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“…Obviously, we can define a Lyapunov function candidate v i j = ε i j ε * i j /2 0 for the i jth subsystem (11), which is positive definite, i.e., v i j > 0 for ε i j = 0 and v i j = 0 for ε i j = 0. Then, we have its time derivative…”

Section: A Complex Znn-i Model For Complex Generalized Inversementioning

confidence: 99%

Different Complex ZFs Leading to Different Complex ZNN Models for Time-Varying Complex Generalized Inverse Matrices

Liao

Zhang

2014

IEEE Trans. Neural Netw. Learning Syst.

147

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As a special class of recurrent neural network, Zhang neural network (ZNN) has been recently proposed since 2001 for solving various time-varying problems, and has shown high efficiency and excellent performance for solving the problems in the real domain. In this paper, to solve online the time-varying complex generalized inverse (in most cases, the pseudoinverse) problem in the complex domain, a new type of complex-valued ZNN is further proposed and investigated. The design of such a complex ZNN is based on a complex Zhang function (ZF) which is indefinite and quite different from the usual error function (specially, the scalar-valued energy function) in the studies of conventional algorithms. By introducing five different complex ZFs, five different complex ZNN models (termed complex ZNN-I, ZNN-II, ZNN-III, ZNN-IV, and ZNN-V models) are proposed, developed, and investigated for the online solution of the time-varying complex generalized inverse matrices. Theoretical results of convergence analysis are presented to show the desirable properties of complex ZNN models. In addition, we discover the link between the proposed complex ZNN models and the Getz-Marsden dynamic system in the complex domain. Computer-simulation results further demonstrate the effectiveness of complex ZNN models based on different complex ZFs for the time-varying complex generalized inverse matrices. Index Terms-Complex-valued Zhang neural network (ZNN), complex Zhang function (ZF), convergence analysis, generalized inverse, pseudoinverse, time-varying complex matrix.

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Reverse order law for the Moore–Penrose inverse

Abstract: In this paper we present new results related to the reverse order law for the MoorePenrose inverse of operators on Hilbert spaces. Some finite-dimensional results are extended to infinite-dimensional settings.

Cited by 63 publications

References 12 publications

Reverse order law for the Moore-Penrose inverse in C*-algebras

Reverse order law for the Moore-Penrose inverse in C*-algebras

A simultaneous canonical form of a pair of matrices and applications involving the weighted Moore–Penrose inverse

Different Complex ZFs Leading to Different Complex ZNN Models for Time-Varying Complex Generalized Inverse Matrices

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