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# Topic: Operator norm

###### In the News (Fri 24 May 13)

 PlanetMath: operator norm must be the zero operator and is assigned zero norm. satisfies all the properties of a norm and hence is called the operator norm (or the induced norm) of This is version 9 of operator norm, born on 2002-06-03, modified 2006-08-14. planetmath.org /encyclopedia/InducedNorm.html   (120 words)

 Examples of Operator Norms (via CobWeb/3.1 planet03.csc.ncsu.edu)   (Site not responding. Last check: 2007-10-10) Theorem 1.2 (The Column-sum norm The operator norm induced by So the operator norm induced by the 1-norm is the maximum value of the sum of the absolute value of the entries in a column. Theorem 1.3 (The Row-sum norm The operator norm induced by web.umr.edu.cob-web.org:8888 /~hilgers/classes/CS328/notes/norm/node7.html   (309 words)

 Bounded operator - Wikipedia, the free encyclopedia (via CobWeb/3.1 planet03.csc.ncsu.edu)   (Site not responding. Last check: 2007-10-10) In functional analysis (a branch of mathematics), a bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded by the same number, over all non-zero vectors v in X. A bounded linear operator is not necessarily a bounded function; the latter would require that the norm of L(v) be bounded for all v. An operator is bounded if it takes every bounded set to a bounded set, and here is meant the more general condition of boundedness for sets in a topological vector space (TVS): a set is bounded if and only if it is absorbed by every neighborhood of 0. en.wikipedia.org.cob-web.org:8888 /wiki/Bounded_operator   (763 words)

 Norm versus operator norm for Banach algebras (via CobWeb/3.1 planet03.csc.ncsu.edu)   (Site not responding. Last check: 2007-10-10) In article , Miguel Carrion wrote: >I forget what the natural norm of (L_1,*) is, It's, err, umm... It's a Banach algebra by that theorem which bounds the L_1 norm of f*g by the product of the L_1 norms of f and g. And it's a B*-algebra because the L_1 norm of the complex conjugate of f equals that of f. www.lns.cornell.edu.cob-web.org:8888 /spr/2003-08/msg0053004.html   (433 words)

 Matrix Norms (via CobWeb/3.1 planet03.csc.ncsu.edu)   (Site not responding. Last check: 2007-10-10) Notice that the definition of a vector norm was tied to the algebraic operations for vectors. What this means is that given a vector norm, they built an operator norm with all of the desired properties including (5). Of course it must be shown that a this defines a matrix norm, which it does. web.umr.edu.cob-web.org:8888 /~hilgers/classes/CS328/notes/norm/node6.html   (282 words)

 Eigenvalue, eigenvector and eigenspace - Wikipedia, the free encyclopedia (via CobWeb/3.1 planet03.csc.ncsu.edu)   (Site not responding. Last check: 2007-10-10) Without damping, the fact that the acceleration operator (assuming a uniform density) is Hermitian leads to several important properties, such as that the standing wave patterns are orthogonal functions. The operator norm of a square matrix is an upper bound for the moduli of its eigenvalues, and thus also for its spectral radius. For normal matrices, the operator norm induced by the Euclidean norm is the largest moduli among its eigenvalues. en.wikipedia.org.cob-web.org:8888 /wiki/Eigenvector   (5236 words)

 Hexapedia - Operator theory (via CobWeb/3.1 planet03.csc.ncsu.edu)   (Site not responding. Last check: 2007-10-10) Operator theory is the branch of functional analysis which deals with bounded linear operators and their properties. It can be split crudely into two branches, although there is considerable overlap and interplay between them. These extend the spectral theory, for bounded operators. operator_theory.en.hexafind.com.cob-web.org:8888   (80 words)

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