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Projections generated by Moore–Penrose inverses and core inverses
Journal of Algebra and Its Applications, 2020Let [Formula: see text] be a unital ∗-ring. As is well known, idempotents and projections can be constructed by the Moore–Penrose inverse and the core inverse of an element in [Formula: see text]. In this paper, we mainly investigate characterizations and properties of these types of idempotents and projections.
Huihui Zhu, Fei Peng
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1997
By definition, a generalized inverse of an m × n matrix A is any n × m matrix G such that AGA = A. Except for the special case where A is a (square) nonsingular matrix, A has an infinite number of generalized inverses (as discussed in Section 9.2a).
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By definition, a generalized inverse of an m × n matrix A is any n × m matrix G such that AGA = A. Except for the special case where A is a (square) nonsingular matrix, A has an infinite number of generalized inverses (as discussed in Section 9.2a).
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The weighted Moore–Penrose inverse of modified matrices
Applied Mathematics and Computation, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Moore--Penrose Inverse of Matrices on Idempotent Semirings
SIAM Journal on Matrix Analysis and Applications, 2000We characterize matrices over an idempotent semiring satisfying some additional necessary conditions for which the Moore--Penrose inverse exists. The "(max,×) semiring," defined as the set of nonnegative real numbers ${\mathbb R}^+,$ equipped with the operations $a\oplus b= \max\{a,b\}\ \mbox{and}\ a\otimes b= ab$ is an example of such a semiring. The "
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Approximating the inverse and the Moore‐Penrose inverse of complex matrices
Mathematical Methods in the Applied Sciences, 2019A parametric family of fourth‐order schemes for computing the inverse and the Moore‐Penrose inverse of a complex matrix is designed. A particular value of the parameter allows us to obtain a fifth‐order method. Convergence analysis of the different methods is studied. Every iteration of the proposed schemes involves four matrix multiplications.
Alicia Cordero +2 more
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More on Moore-Penrose Inverses
1979The various properties of A+ discussed in this section are fundamental to the theory of Moore-Penrose inverses. In many cases, proofs simply require verification that the defining equations in (2.2) are satisfied for A and some particular matrix X.
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Do All Dual Matrices Have Dual Moore–Penrose Generalized Inverses ?
Mechanism and Machine Theory, 2020Ettore Pennestrì, Domenico De Falco
exaly