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May 15th, 2011, 06:37 AM   #1
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Frobenius norm


I am a newbie to this Forum.
I would to ask you about Frobenius Norm?
What is its utility. What it is measuring (not the formula, but the its meaning).

Thank you.
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May 15th, 2011, 08:24 AM   #2
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Re: Frobenius norm


Welcome to the forum.

The Frobenius norm is the -norm on the space of matrices of a given shape. In other words, you interpret the matrix as a large vector, and compute the norm in the usual Euclidean way. I suppose that since this norm is expressed solely in terms of the entries of the matrix, it is appealing for applications. I believe it is "sub-multiplicative", meaning it satisfies

which can be a good property to have.

As for what it means, it is merely a way to assign a size to a matrix. There are other good norms for matrices, all with slightly different properties and optimal uses. Did you have some specific property of the Frobenius norm as compared to other norms in mind with this question?

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May 29th, 2011, 02:25 AM   #3
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Re: Frobenius norm

I am very thankful
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