# norm

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Related to normed: Normed linear space, Normed vector space

## norm,

authoritative rule or standard by which something is judged and on that basis approved or disapproved. Examples of norms include standards of right and wrong, beauty and ugliness, and truth and falsehood. Several fields of philosophy, especially ethics**ethics,**

in philosophy, the study and evaluation of human conduct in the light of moral principles. Moral principles may be viewed either as the standard of conduct that individuals have constructed for themselves or as the body of obligations and duties that a particular society

**.....**Click the link for more information. , aesthetics

**aesthetics**

, the branch of philosophy that is concerned with the nature of art and the criteria of artistic judgment. The classical conception of art as the imitation of nature was formulated by Plato and developed by Aristotle in his

*Poetics,*

**.....**Click the link for more information. , and logic

**logic,**

the systematic study of valid inference. A distinction is drawn between logical validity and truth. Validity merely refers to formal properties of the process of inference.

**.....**Click the link for more information. , evaluate such rules; in sociology, social and institutional norms, more communal and less formal than laws, are studied in relation to conformity, and to anomie or normlessness. See also Émile Durkheim

**Durkheim, Émile**

, 1858–1917, French sociologist. Along with Max Weber he is considered one of the chief founders of modern sociology. Educated in France and Germany, Durkheim taught social science at the Univ. of Bordeaux and the Sorbonne.

**.....**Click the link for more information. .

## norm

a standard or rule, regulating behaviour in a social setting. The idea that social life, as an ordered and continuous process, is dependent upon shared expectations and obligations, is commonly found in sociological approaches, although some place more emphasis on it than others. For DURKHEIM, society was theorized as a moral order. This perspective was influential in the development of modern FUNCTIONALISM, particularly in the work of PARSONS, where the concept of NORMATIVE ORDER is the central element of the SOCIAL SYSTEM. Here the idea of norms is related to SOCIALIZATION and ROLES. These prescriptions operate at every level of society, from individuals actions in daily life, e.g. in table manners or classroom behaviour, to the formulation of legal systems in advanced societies. The concept of norms also implies that of SOCIAL CONTROL, i.e. positive or negative means of ensuring conformity and applying sanctions to deviant behaviour (see DEVIANCE).Other sociological approaches deal with the issue of social order in rather different ways. In some, RULES are emphasized, rather than norms, whilst in others there is a greater emphasis on POWER and coercion.

## Norm

**(1)** The minimum of something, as established by a rule or plan, for example, a time norm or sowing norm.

**(2)** A rule or viewpoint generally accepted in a particular social milieu; a rule of social conduct expressed in a law (legal norm).

**(3)** A rule or law in some branch of learning, for example, a linguistic norm.

**(4)** The average of something, such as a flow norm.

**(5)** Norm of representation, the number of deputies or delegates representing a preestablished number of voters in elective bodies or at congresses and conferences.

**(6)** Typographic norm, the title of a book or the name of its author, printed in small type on the first page of every printed sheet.

## Norm

a mathematical concept that generalizes the concept of the absolute value of a number. For example, the norm of a vector x is the length of the vector and is denoted by ǀǀ*x*ǀǀ. The norm of a quaternion *a + bi + cj + dk* is the number *a*^{2} + *b*^{2} + *c*^{2} + *d*^{2}; the norm of a matrix *A* is the number

and the norm of an algebraic number is the product of all the numbers conjugated with it, including the number itself. The norm is used extensively in the theory of linear spaces. We can find the norm for linear functionals in a given linear space according to the formula

and for linear operators according to the formula

## norm

[nȯrm]## norm

**1.**

*Maths*

**a.**the length of a vector expressed as the square root of the sum of the square of its components

**b.**another name for mode

**2.**

*Geology*the theoretical standard mineral composition of an igneous rock

## norm

(mathematics)The most popular norm is the Euclidean norm.