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metric

1. of or relating to the metre or metric system
2. Maths denoting or relating to a set containing pairs of points for each of which a non-negative real number ρ(x, y) (the distance) can be defined, satisfying specific conditions
3. Maths the function ρ(x, y) satisfying the conditions of membership of such a set (a metric space)

Metric

 

a mathematical term that denotes the rule for determining a given distance between any two points (elements) of a given set A. A real number function that satisfies the following three conditions is called the distance ρ (a, b) between the points a and b of the set A: (1) ρ (a, b) ≧ 0, where ρ(a, b) = 0 if and only if a = b; (2) ρ(a, b) = ρ(b, a); and (3) ρ(a, b) + ρ(b, c) ≧ ρ(a, c). For a given set M, a metric may be introduced in other ways. For example, on a plane we may take not only the ordinary Euclidean distance

as the distance between points a and b having coordinates (x1, y1) and (x2, y2), respectively, but we may take other distances as well, for example,

ρ1(a, b) = ǀx1x2ǀ + ǀy1y2ǀ

In (functional and coordinate) vector spaces a metric is often defined as a norm or, sometimes, as a scalar product. In differential geometry, a metric is introduced by specifying an element of arc length by means of a differential quadratic form. A set that has a metric introduced in it is referred to as a metric space.

A metric is sometimes understood to denote a rule for determining not only distances but also angles; an example is a projective metric.

V. I. SOBOLEV

metric

[′me·trik]
(mathematics)
A real valued “distance” function on a topological space X satisfying four rules: for x, y, and z in X, the distance from x to itself is zero; the distance from x to y is positive if x and y are different; the distance from x to y is the same as the distance from y to x ; and the distance from x to y is less than or equal to the distance from x to z plus the distance from z to y (triangle inequality).

metric

metric

Measurement. Although metric generally refers to a system of weights and measures, software engineers often use the term as simply "measurement." For example, "is there a metric for this process?" See software metrics.
References in periodicals archive ?
The possibility of metrically significant simultaneities is reduced as a result.
Pipes and Drums is written in middle-C position and notated metrically with noteheads and alphabet letters.
Finch's theory of the "metrical code," which "implies that meter in a metrically organic poem can function like a language" (12), enables her to argue that meter enacts meaning not just situationally or tactically, but at the larger relational level of cultural intertextuality.
Susan Peter, Head of Marketing, Simcorp, North America, comments, "I am very metrically driven and believe you have to be able to measure what you are managing.
At the close of the article, Wen speculates that Brahms's use of a metrically recast version of his song, "Wie Melodien zieht es mir" (op.
The verse repeated at every line the act of integrity required to think metrically without relapsing into an automatism of register.
In the Cancionero capitular the third line of the first verse is metrically imperfect ('non contrastes las gentes', p.
Most arrangements are in original keys, while some, for example Dvorak's Largo from New World Symphony, have been metrically simplified for reading ease.
Fast, deep, strong and metrically tricky, this exciting, 19-minute performance is the album's tour de force.
He sees this system as contributing to the "sheer cantabile quality of their music," a quality he presumably wishes to be reflected in the translations with the use of a metrically based line division.
Enriching the limited repertoire for these three instruments, Conservatoire student Paul McKinley's Acorn Trio , winner of the first BCMS Composition Prize, was here given a well-prepared premiere, metrically well-defined and beautifully paced as it assimilates ethnic and jazzy elements, the piece has obviously been conceived with great clarity of thought and execution.
Metrical emendations are avoided, grammatically and metrically warranted final e not present in F being added only where other witnesses do so.