Moore–Penrose-invertible normal and Hermitian elements in rings
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In this paper, the authors presented several new characterizations of normal and Hermitian elements in rings with involution in purely algebraic terms, and considerably simplify proofs of existing characterizations.About:
This article is published in Linear Algebra and its Applications.The article was published on 2009-08-01 and is currently open access. It has received 44 citations till now. The article focuses on the topics: Invertible matrix & Hermitian matrix.read more
Citations
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The effect of machine learning regression algorithms and sample size on individualized behavioral prediction with functional connectivity features.
TL;DR: Critical insight is provided into how the selectedML regression algorithm and sample size influence individualized predictions of behavior/cognition and offer important guidance for choosing the ML regression algorithm or sample size in relevant investigations.
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Partial isometries and EP elements in rings with involution
TL;DR: In this article, characterizations of partial isometries, EP elements and star-dagger elements in rings with involution are given, and some well-known results are extended to more general settings.
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Further results on partial isometries and EP elements in rings with involution
TL;DR: This work investigates elements in rings with involution which are EP or partial isometries, and some well-known results are generalized.
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Reverse order law for the Moore-Penrose inverse in C*-algebras
TL;DR: In this article, the reverse order rule for the weighted Moore-Penrose inverse in C∗-algebras was studied and several equivalent conditions related to reverse order law were derived.
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New characterizations of EP, generalized normal and generalized Hermitian elements in rings
TL;DR: A number of new characterizations of normal and Hermitian elements in rings with involution in purely algebraic terms are presented.
References
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Book
Generalized inverses: theory and applications
Adi Ben-Israel,T. N. E. Greville +1 more
TL;DR: In this paper, the Moore of the Moore-Penrose Inverse is described as a generalized inverse of a linear operator between Hilbert spaces, and a spectral theory for rectangular matrices is proposed.
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A Generalized inverse for matrices
TL;DR: A generalization of the inverse of a non-singular matrix is described in this paper as the unique solution of a certain set of equations, which is used here for solving linear matrix equations, and for finding an expression for the principal idempotent elements of a matrix.
Book
Matrix Theory: Basic Results and Techniques
TL;DR: In this paper, the authors present an elementary linear algebra review of the second edition of the Second Edition of the Basic Linear Algebra (BLA) and discuss the use of matrix polynomials and Canonical forms.
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Pseudo-Inverses in Associative Rings and Semigroups
TL;DR: In this paper, Pseudo-inverses in Associative Rings and Semigroups are discussed in the context of semigroups, and pseudo-Inverses are shown to be pseudo-dual in a semigroup.