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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, 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.
Note that the definition of uniform norm does not rely on any additional structure on the set , although in practice is often at least a topological space. The convergence on Y X {\displaystyle Y^{X}} in the topology induced by the uniform extended norm is the uniform convergence , for sequences, and also for nets and filters on Y X ...
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
In commutative algebra, the norm of an ideal is a generalization of a norm of an element in the field extension.It is particularly important in number theory since it measures the size of an ideal of a complicated number ring in terms of an ideal in a less complicated ring.
Operator norm, a map that assigns a length or size to any operator in a function space; 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