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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.
Download as PDF; Printable version; In other projects ... Symbol sets: Linear B Greek: Assigned: 123 code points: ... L2 ID WG2 ID Document 4.0:
By Dvoretzky's theorem, every finite-dimensional normed vector space has a high-dimensional subspace on which the norm is approximately Euclidean; the Euclidean norm is the only norm with this property. [24] It can be extended to infinite-dimensional vector spaces as the L 2 norm or L 2 distance. [25]
Norm (mathematics)#Euclidean norm To a section : This is a redirect from a topic that does not have its own page to a section of a page on the subject. For redirects to embedded anchors on a page, use {{ R to anchor }} instead .
Download as PDF; Printable version; In other projects ... -norm or maximum norm (or uniform norm) is the limit of the ... "L1 penalty" and "L2 penalty" refer to ...
The norm (see also Norms) can be used to approximate the optimal norm via convex relaxation. It can be shown that the L 1 {\displaystyle L_{1}} norm induces sparsity. In the case of least squares, this problem is known as LASSO in statistics and basis pursuit in signal processing.
The Frobenius norm defined by ‖ ‖ = = = | | = = = {,} is self-dual, i.e., its dual norm is ‖ ‖ ′ = ‖ ‖.. The spectral norm, a special case of the induced norm when =, is defined by the maximum singular values of a matrix, that is, ‖ ‖ = (), has the nuclear norm as its dual norm, which is defined by ‖ ‖ ′ = (), for any matrix where () denote the singular values ...