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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. Regularization (mathematics) - Wikipedia

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

    The norm (see also Norms) can be used to approximate the optimal norm via convex relaxation. It can be shown that the norm induces sparsity. In the case of least squares, this problem is known as LASSO in statistics and basis pursuit in signal processing.

  5. 10 Hard Math Problems That Even the Smartest People in the ...

    www.aol.com/10-hard-math-problems-even-150000090...

    The Kissing Number Problem. A broad category of problems in math are called the Sphere Packing Problems. They range from pure math to practical applications, generally putting math terminology to ...

  6. Category:Norms (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Category:Norms_(mathematics)

    Pages in category "Norms (mathematics)" The following 20 pages are in this category, out of 20 total. This list may not reflect recent changes. ...

  7. Distortion problem - Wikipedia

    en.wikipedia.org/wiki/Distortion_problem

    In functional analysis, a branch of mathematics, the distortion problem is to determine by how much one can distort the unit sphere in a given Banach space using an equivalent norm. Specifically, a Banach space X is called λ-distortable if there exists an equivalent norm |x| on X such that, for all infinite-dimensional subspaces Y in X,

  8. 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 .

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