Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the authors give shorter proofs of some properties of real symmetric idempotent matrices, which are suggested by the fact that these matrices represent projection operators, and by known properties of such operators.
Abstract: Banerjee [1] has recently given proofs of various properties of real symmetric idempotent matrices The aim of this note is to give shorter proofs of some of these Some of our proofs are suggested by the fact that idempotent matrices represent projection operators, and by the known properties of such operators (see eg Halmos [2]) The recent paper by Luther [4] overlaps this note in content; but has a different aim
7 citations
TL;DR: In this article, it was shown that a nonzero idempotent is zero-diagonal if and only if it is not a Hilbert-Schmidt perturbation of a projection, along with other useful equivalences.
Abstract: We prove that a nonzero idempotent is zero-diagonal if and only if it is not a Hilbert-Schmidt perturbation of a projection, along with other useful equivalences. Zero-diagonal operators are those whose diagonal entries are identically zero in some basis.
We also prove that any bounded sequence appears as the diagonal of some idempotent operator, thereby providing a characterization of inner products of dual frame pairs in infinite dimensions. Furthermore, we show that any absolutely summable sequence whose sum is a positive integer appears as the diagonal of a finite rank idempotent.
7 citations
Journal Article•
TL;DR: In this article, Pin's refinement of Eilenberg theorem gives a one-to-one correspondence between positive varieties of rational languages and pseudovarieties of ordered monoids.
Abstract: A classical construction assigns to any language its (ordered) syntactic monoid. Recently the author defined the so-called syntactic semiring of a language. We discuss here the relationships between those two structures. Pin's refinement of Eilenberg theorem gives a one-to-one correspondence between positive varieties of rational languages and pseudovarieties of ordered monoids. The author's modification uses so-called conjunctive varieties of rational languages and pseudovarieties of idempotent semirings. We present here also several examples of our varieties of languages.
7 citations
TL;DR: The role of idempotent elements and atoms in the theory of ideal and filter in D-posets is studied in this paper, where the authors define the notion of ideal elements and filters.
Abstract: Ideals and filters in D-posets are defined. Therole of idempotent elements and atoms in the theory ofideals and filters is studied.
7 citations
Journal Article•
TL;DR: In this article, a simplicial idempotent augmented endof-unctor was constructed under the assumption of Vopenka's principle, such that the cellularization with respect to the cofibrant objects in the simplicial combinatorial model category was obtained.
Abstract: Given a simplicial idempotent augmented endofunctor $F$ on a simplicial combinatorial model category $M$, under the assumption of Vopenka's principle, we exhibit a set $A$ of cofibrant objects in $M$ such that $F$ is equivalent to $\CW_A$, the cellularization with respect to $A$.
7 citations