Frobenius product

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


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.

Title Frobenius product
Canonical name FrobeniusProduct
Date of creation 2013-03-22 18:11:34
Last modified on 2013-03-22 18:11:34
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 8
Author pahio (2872)
Entry type Definition
Classification msc 15A60
Classification msc 15A63
Synonym Frobenius inner product
Related topic NormedVectorSpace
Related topic FrobeniusMatrixNorm
Related topic Product
Defines Frobenius norm