# idempotent

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## idempotent

(ˈaɪdəmˌpəʊtənt; ˈɪd-)
(Mathematics) maths (of a matrix, transformation, etc) not changed in value following multiplication by itself
[C20: from Latin idem same + potent1]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## i•dem•po•tent

(ˈaɪ dəmˈpoʊt nt, ˈɪd əm-)
1. (of a number or matrix) unchanged when multiplied by itself.
n.
2. an idempotent element.
[1870; idem + potent1]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Adj. 1 idempotent - unchanged in value following multiplication by itself; "this matrix is idempotent"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementunchanged - not made or become different; "the causes that produced them have remained unchanged"
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
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References in periodicals archive ?
Recall that a matrix A in [M.sub.n](L) is called idempotent if [A.sup.2] = A.
Let S be a regular semigroup with set E(S) of idempotent elements.
Contrary to the orthogonal projection is idempotent and Hermitian, the oblique one is idempotent and not Hermitian.
Since the mapping [sigma] is idempotent, [sigma]([empty set]) = S and [sigma]([H.sub.1] [union] [H.sub.2]) = [sigma]([H.sub.1]) [intersection] [sigma]([H.sub.2]) for all [H.sub.1], [H.sub.2] [member of] S, the proof is clear.
Let t be the smallest positive integer for which [r.sup.t] is idempotent for every r [member of] [R.sub.c] and the exponent of G divides t.
If e is an idempotent of T and [f.sup.-1](e) is nonempty then [f.sup.-1](e) is an inverse sub semigroup of S.
In particular, they are idempotent and they follow the semi-group absorption law, i.e., [for all] n [greater than or equal to] m [greater than or equal to] 0,we have
Now we have the fact that for any idempotent e, d(y(1 - e))e = -y(1 - e)d(e), ed(e)e = 0 and so
Lemma 4: Let e be an idempotent in A and let V be an A module.
The time series of discriminants (dsk [M.sub.n]), discriminant coefficients (dskCoeff [M.sub.n]) and idempotent coefficients (IdeCoeff [M.sub.n]) are calculated from two time series: duration of RR interval taken from the II standard lead and duration of JT interval of the V standard lead.

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