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In mathematics, a norm is a function from a real or complex vector space to the non ... Some authors include non-negativity as part of the definition of "norm ...
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.
In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz ().
In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. [1] A norm is a generalization of the intuitive notion of "length" in the physical world.
In mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces .
In mathematics, the (field) norm is a particular mapping defined in field theory, which maps elements of a larger field into a subfield. Formal definition
Norm (abelian group), a map that assigns a length or size to any element of an abelian group; Field norm a map in algebraic number theory and Galois theory that generalizes the usual distance norm; Ideal norm, the ideal-theoretic generalization of the field norm; Norm (group), a certain subgroup of a group; Norm map, a map from a pointset into ...
More generally, given any centrally symmetric, bounded, open, and convex subset X of R n, one can define a norm on R n where the balls are all translated and uniformly scaled copies of X. Note this theorem does not hold if "open" subset is replaced by "closed" subset, because the origin point qualifies but does not define a norm on R n.