# 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 ?
This will influence the perception of metrical structures, which leads us to think that performers, in addition to having the general qualities of the human being for musical perception, will be conditioned by their own experience and by their degree of musical training.
Hence, the metrical structure of the genitive singular assumes a greater role in identifying class outside the first declension.
The metrical structure of Takituduh is not constrained syllabically either, since [FTBIN.
This enables the performer to give an individual interpretation of a folk song without any restriction from constant pulse or metrical structure.
This arrangement brings to mind not only rococo metrical structure, but also that of rococo ornamentation: there are mirror images, but rather than a perfect symmetry which is sustained from beginning to end as one would expect in a classical garden, (20) the possibility of a strictly classical structure in Psyche dissolves through metonymy into arabesques and organic rocaille (Brady, Rococo Style 55).
Metrical structure in the shipboard compositions, as elsewhere, avails a framework for feeling at home in a poem, whether one recognizes the specific referent--here Hood's poem, which itself echoes Tennyson's 1842 "Break, Break, Break"--or not.
Indeed, Evans makes clear that evidence of metrical structure, however partial and interrupted, raises more questions than it answers.
These findings suggest that for the highly complex artistic movements involved in dance, beginners perform much better to a rhythmical sequence of single beats than when guided by a musical phrase having identical metrical structure.
This originated in a mistaken view of the Greek texts, whose metrical structure is much stricter than Renaissance editors and readers supposed.
We base our analysis of metrical structure directly on the prosodic hierarchy (Selkirk 1978, 1980, 1981, 1986, 1995; Nespor and Vogel 1982, 1986; Hayes 1989) and assume that metrical structure bears a strict relation to the prosodic structure of natural language (Jakobson 1933, 1952; Kiparsky 1975, 1977; Nespor and Vogel 1986: chapter 10; Hayes 1989; Helsloot 1995, 1997; Golston and Riad 1997; Golston 1998).
116) - may prove to be a stumbling block for readers who understand ambiguity as enriching rather than disrupting a hierarchic metrical structure.
Most practitioners are happy for their investigations of texts to be framed by traditional literary categories such as point of view, metrical structure, and metaphor; and where the range of literary concepts has been extended by ideas from linguistics and related fields, e.

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