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

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 ?
In (1), we see that the traditional scansion (7) gives the metrical structure [?
In the new study, researchers at Cambridge have shown, using a music task, that this is linked to a broader difficulty in perceiving rhythmic patterns, or metrical structure.
Compared to the E/Z plays, the metrical structure of JerLib presents several obvious anomalies.
Hence, gradation complements the class information cued by metrical structure, much like other class-specific patterns.
In order to show how syllabic considerations affect the metrical structure of Isbukun, this section will first present an overview of Isbukun phonemes and syllables (Section 2.
2002a 'Segmental evidence for metrical structure in Iwaidja', paper presented to Speech Science and Technology Conference, Melbourne.
The metre and bar structures of Sharp's notated version remain largely unchanged in Fairport Convention's recording of the song, and the drum kit arrangement supports the melody and follows the notated metrical structure while providing a constant pulse and maintaining an authentic rock music context.
Sam Hamill agrees, but he thinks that ignoring the syllabic structure of haiku and tanka sacrifices "the musicality that may be achieved by adhering to form"--though he has already noted how attempts to imitate the rhymed, metrical structure of classical Chinese "have largely resulted in academic doggerel.
Modern poetry needs explication, and its metrical structure is often anyone's guess, and it emerged at the moment when the explication of vernacular poetry became a profession.
One reason for this is the premise of the entire project, stated at the outset: "If we assume that harmony, metrical structure, and the like are real and important factors in musical listening, then listening must involve extracting this information from the incoming notes.
He writes: "Many of the day-to-day tasks which people carry out in the countryside have poetry associated with them in the form of work songs, each type with its own metrical structure and associated tunes.