Norm (redirected from norming)

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, aesthetics, and logic, 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.

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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

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norm [nȯrm]

(mathematics)

A scalar valued function on a vector space with properties analogous to those of the modulus of a complex number; namely: the norm of the zero vector is zero, all other vectors have positive norm, the norm of a scalar times a vector equals the absolute value of the scalar times the norm of the vector, and the norm of a sum is less than or equal to the sum of the norms.

For a matrix, the square root of the sum of the squares of the moduli of the matrix entries.

For a quaternion, the product of the quaternion and its conjugate.

absolute value

(metallurgy)

fineness

(petrology)

The theoretical mineral composition of a rock expressed in terms of standard mineral molecules as determined by means of chemical analyses.

(quantum mechanics)

The square of the modulus of a Schrödinger-Pauli wave function, integrated over the space coordinates and summed over the spin coordinates of the particles it describes.

The square root of this quantity.

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(mathematics)

norm - A real-valued function modelling the length of a vector. The norm must be homogeneous and symmetric and fulfil the following condition: the shortest way to reach a point is to go straight toward it. Every convex symmetric closed surface surrounding point 0 introduces a norm by means of Minkowski functional; all vectors that end on the surface have the same norm then. The most popular norm is the Euclidean norm.

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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.

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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 ǀǀxǀǀ. The norm of a quaternion a + bi + cj + dk is the number a² + b² + c² + d²; 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