# metric

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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

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 ?
Not only are intermediate projections metrically invisible, but nodes that have been treated as weak in metrical theories (Liberman 1975; Liberman and Prince 1977; Ladd 1980) are claimed to be metrically invisible in Zubizarreta's theory as well (see [37b]).
This shifting of gatra from metrically weak to strong parts of the formal structure is a favorite trick of Javanese composers as well, as Jody Diamond points out, comparing Bubaran Robert to Bubaran Rediguntur, a traditional piece.
Both passages will pass the Halle-Keyser test for metricity--and probably every other generative test as well--but only one is presented so as to be read metrically, that is, with more regular and frequent stressing, and, I would argue, light pauses to indicate line endings.
Rig Veda: A Metrically Restored Text with an Introduction and Notes.
In the third line, the prolonged, five-beat line, ending with two rhythmically promoted monosyllables in the cliched "to and fro," enacts metrically merely the desultory and pointless, unmeaning, protraction of words that is the fruitless conversation of the couple.
As a result, an increasing volume of such local structure with respect to the electrical field results in an observable metrically tetragonal phase.
Whilst metrically insightful, his reading of "Le Bateau ivre" is uncontroversially posited on the precariousness of interpretation.
257), in particular, allows Murphy some convincing thematic interpretations of metrically problematic lines.
My only complaint is that nowadays they stop metrically at 10, instead of going on to 12.
Many need to be scaled up or down to fit metrically. Forget rhyme.
Although sweets are weighed metrically, as befits EU rules, they are also sold by the quarter with a quarter of an ounce of toffee bonbons costing 69p.
Along the way she restores to this umanista dimenticato a number of conjectures generally credited to later scholars which in her view show "good powers of divination" as being reasonable, even ingenious, paleographically possible, and metrically acceptable.

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