inverse

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inverse

1. Maths
a. (of a relationship) containing two variables such that an increase in one results in a decrease in the other
b. (of an element) operating on a specified member of a set to produce the identity of the set: the additive inverse element of x is --x, the multiplicative inverse element of x is 1/x
2. Maths
a. another name for reciprocal
b. an inverse element
3. Logic a categorial proposition derived from another by changing both the proposition and its subject from affirmative to negative, or vice versa, as all immortals are angels from no mortals are angels
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

inverse

[′in‚vərs]
(mathematics)
The additive inverse of a real or complex number a is the number which when added to a gives 0; the multiplicative inverse of a is the number which when multiplied with a gives 1.
The inverse of a fractional ideal I of an integral domain R is the set of all elements x in the quotient field K of R such that xy is in I for all y in I.
For a set S with a binary operation x · y that has an identity element e, the inverse of a member, x, of S is another member, , of S for which x · = · x = e.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

inverse

(mathematics)
Given a function, f : D -> C, a function g : C -> D is called a left inverse for f if for all d in D, g (f d) = d and a right inverse if, for all c in C, f (g c) = c and an inverse if both conditions hold. Only an injection has a left inverse, only a surjection has a right inverse and only a bijection has inverses. The inverse of f is often written as f with a -1 superscript.
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)
References in periodicals archive ?
Stanimirovic, "A note on the stability of a th order iteration for finding generalized inverses," Applied Mathematics Letters, vol.
In recent years, the generalized inverse has been applied in many fields of engineering and technology, such as control [1], the least squares problem [2, 3], matrix decomposition [4], image restoration, statistics (see [5]), and preconditioning [6-8].
(ii) The time needed to obtain the approximate inverses is reported in seconds.
On the other hand, since the generation of random square matrices having Drazin inverses is difficult, in what follows, we compare various competitors in terms of the elapsed computational time so as to attain regular approximate inverses for large sparse matrices.
Conditions for the existence and representations of generalized inverses included in (4) are given in Section 2.
Theorem 3 provides a theoretical basis for computing outer inverses with the prescribed range space.
The new iteration (9) is free from matrix power in its implementation and this allows one to apply it for finding generalized inverses easily.
In Algorithm 2, we provide the written Mathematica 8 code of the new scheme (9) in this example to clearly reveals the simplicity of the new scheme in finding approximate inverses using a threshold Chop[exp, [10.sup.-10]].
Computing the matrix inverse of nonsingular matrices of higher sizes is difficult and is a time consuming task.
Many real-world inverse problems are nonlinear and unlike the linear ones have not been fully explored due to the complexity of the problem.
In this paper we consider compact sets K and partial differential operators P(D) such that there exists a continuous linear right inverse [??] for P(D) on [epsilon]([R.sup.n]) so that [??]([I.sub.K]) [subset of equal to] [I.sub.K] ([I.sub.K] stands for the ideal of functions flat on K).
[3] Let (S, (x), [less than or equal to]) be a partially ordered inverse semigroup.