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  2. Norm (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Norm_(mathematics)

    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.

  3. Matrix norm - Wikipedia

    en.wikipedia.org/wiki/Matrix_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.

  4. Hilbert symbol - Wikipedia

    en.wikipedia.org/wiki/Hilbert_symbol

    The Hilbert symbol can also be used to denote the central simple algebra over K with basis 1,i,j,k and multiplication rules =, =, = =.In this case the algebra represents an element of order 2 in the Brauer group of K, which is identified with -1 if it is a division algebra and +1 if it is isomorphic to the algebra of 2 by 2 matrices.

  5. Symbol (number theory) - Wikipedia

    en.wikipedia.org/wiki/Symbol_(number_theory)

    Norm residue symbol This name is for several different closely related symbols, such as the Artin symbol or the Hilbert symbol or Hasse's norm residue symbol. The Hasse norm residue symbol ((, /) /) = (, /) is defined if p is a place of K and α an element of K. It is essentially the same as the local Artin symbol for the localization of K at p ...

  6. Operator norm - Wikipedia

    en.wikipedia.org/wiki/Operator_norm

    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 .

  7. Glossary of mathematical symbols - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...

  8. Normed vector space - Wikipedia

    en.wikipedia.org/wiki/Normed_vector_space

    A norm induces a distance, called its (norm) induced metric, by the formula (,) = ‖ ‖. which makes any normed vector space into a metric space and a topological vector space. If this metric space is complete then the normed space is a Banach space .

  9. Vector notation - Wikipedia

    en.wikipedia.org/wiki/Vector_notation

    The norm of a vector is represented with double bars on both sides of the vector. The norm of a vector v can be represented as: ‖ ‖ The norm is also sometimes represented with single bars, like | |, but this can be confused with absolute value (which is a type of norm).