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单词 FrobeniusProduct
释义

Frobenius product


If  A=(aij)  and  B=(bij)  are real m×n matrices, their Frobenius product is defined as

A,BF:=i,jaijbij.

It is easily seen that  A,BF  is equal to the trace of the matrix AB and AB, and that the Frobenius product is an inner product of the vector spaceMathworldPlanetmath formed by the m×n matrices; it the Frobenius norm of this vector space.

TitleFrobenius product
Canonical nameFrobeniusProduct
Date of creation2013-03-22 18:11:34
Last modified on2013-03-22 18:11:34
Ownerpahio (2872)
Last modified bypahio (2872)
Numerical id8
Authorpahio (2872)
Entry typeDefinition
Classificationmsc 15A60
Classificationmsc 15A63
SynonymFrobenius inner product
Related topicNormedVectorSpace
Related topicFrobeniusMatrixNorm
Related topicProduct
DefinesFrobenius norm
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更新时间:2025/5/4 18:05:23