Metric (redirected from metrical)

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.

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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)

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metric [′me·trik]

(mathematics)

A real valued “distance” function on a topological spaceXsatisfying four rules: forx, y,andzinX,the distance fromxto itself is zero; the distance fromxtoyis positive ifxandyare different; the distance fromxtoyis the same as the distance fromytox; and the distance fromxtoyis less than or equal to the distance fromxtozplus the distance fromztoy(triangle inequality).

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metric - software metric

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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) = ǀx₁ – x₂ǀ + ǀy₁ – y₂ǀ

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