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A note on generalized inverses [PDF]
Mathematical Methods of Operations Research, 2013 ISSN:1432 ...
Paul Embrechts, Marius Hofert
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Open Journal of Mathematical Optimization, 2021 The M-P (Moore–Penrose) pseudoinverse has as a key application the computation of least-squares solutions of inconsistent systems of linear equations. Irrespective of whether a given input matrix is sparse, its M-P pseudoinverse can be dense, potentially
Fampa, Marcia, Lee, Jon, Ponte, Gabriel
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The dual index and dual core generalized inverse
Open Mathematics, 2023 In this article, we introduce the dual index and dual core generalized inverse (DCGI). By applying rank equation, generalized inverse, and matrix decomposition, we give several characterizations of the dual index when it is equal to 1. We realize that if
Wang Hongxing, Gao Ju
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Closed-form formula for a classical system of matrix equations
Arab Journal of Basic and Applied Sciences, 2022 Keeping in view the latest development of anti-Hermitian matrix in mind, we construct some closed form formula for a classical system of matrix equations having anti-Hermitian nature in this paper.
Abdur Rehman +4 more
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Proceedings of the American Mathematical Society, 1988 Let A A be a (possibly unbounded) linear operator on a Banach space X X that generates a bounded holomorphic semigroup of angle θ ( 0 > θ ≤ π / 2 ) \theta (0 > \theta \leq \pi /2) . We show that, if the range of
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The generalized S- and σ-inverse – a comparative case study for right- and left-invertible plants [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2020 In this paper, an advanced study covering the comparison between two classes of generalized inverses is conducted. Two sets of instances, strictly derived from the recently introduced nonunique S- and σ-inverse, are analyzed, especially in terms of ...
P. Majewski, W.P. Hunek
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Higher Regularity, Inverse and Polyadic Semigroups
Universe, 2021 We generalize the regularity concept for semigroups in two ways simultaneously: to higher regularity and to higher arity. We show that the one-relational and multi-relational formulations of higher regularity do not coincide, and each element has several
Steven Duplij
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Formal inverses of the generalized Thue-Morse sequences and variations of the Rudin-Shapiro sequence [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A formal inverse of a given automatic sequence (the sequence of coefficients of the composition inverse of its associated formal power series) is also automatic.
Łukasz Merta
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(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup [PDF]
Categories and General Algebraic Structures with Applications, 2021 We prove that the (b, c)-inverse and the inverse along an element in a semigroup are actually genuine inverse when considered as morphisms in the Schützenberger category of a semigroup. Applications to the Reverse Order Law are given.
Xavier MARY
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The reverse order law for the generalized Bott-Duffin inverses of matrices
上海师范大学学报. 自然科学版, 2019 In this paper we investigate the reverse order law for the generalized Bott-Duffin inverses of two L-p.s.d.matrices.The concept of L-p.s.d.matrices is a generalization of semi-positive definiteness,in the sense that Rn-p.s.d.matrices are exactly semi ...
CAO Zhiqiang, DU Nailin
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