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In Deep Learning section 2.5 the author review some measures for the size of vectors and matrices.

When in general is it useful for someone to know these?

For instance they give the example of the Frobenius Norm which is analogous to the L2 Norm for matrices. Is this a metric that is more used in academics?

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It is basically a similarity measure for matrices. There are multiple uses for Frobenius Norm, some examples could be classifying covariance matrices for action recognition and low-rank bilinear pooling.

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