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In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin.
Norm map, a map from a pointset into the ordinals inducing a prewellordering Norm group , a group in class field theory that is the image of the multiplicative group of a field Norm function, a term in the study of Euclidean domains , sometimes used in place of "Euclidean function"
Suppose a vector norm ‖ ‖ on and a vector norm ‖ ‖ on are given. Any matrix A induces a linear operator from to with respect to the standard basis, and one defines the corresponding induced norm or operator norm or subordinate norm on the space of all matrices as follows: ‖ ‖, = {‖ ‖: ‖ ‖ =} = {‖ ‖ ‖ ‖:} . where denotes the supremum.
The norm on the left is the one in and the norm on the right is the one in . Intuitively, the continuous operator never increases the length of any vector by more than a factor of . Thus the image of a bounded set under a continuous operator is also bounded.
The perimeter of the square is the set of points in ℝ 2 where the sup norm equals a fixed positive constant. For example, points (2, 0), (2, 1), and (2, 2) lie along the perimeter of a square and belong to the set of vectors whose sup norm is 2.
A social norm is a shared standard of acceptable behavior by a group. [1] Social norms can both be informal understandings that govern the behavior of members of a ...
Such norm sentences do not describe how the world is, they rather prescribe how the world should be. Imperative sentences are the most obvious way to express norms, but declarative sentences also may be norms, as is the case with laws or 'principles'. Generally, whether an expression is a norm depends on what the sentence intends to assert.
A convention influences a set of agreed, stipulated, or generally accepted standards, social norms, or other criteria, often taking the form of a custom.. In physical sciences, numerical values (such as constants, quantities, or scales of measurement) are called conventional if they do not represent a measured property of nature, but originate in a convention, for example an average of many ...