Comment #13 on issue 2225 by [email protected]: Enhancing Matrix Norm http://code.google.com/p/sympy/issues/detail?id=2225
What I mean is, Norms make sense only when the matrix is completely known, and thus when it is purely numerical. 'Norm' aims to associate a number with a matrix that is a reasonable measure of its largeness, so that we can compare matrices. Adding norm to symbolic matrices is not very useful, since most norm definitions are eigenvalue-based algorithms, which itself is a purely numerical matrix property. We can however implement some trivial norms, which are not based on eigenvalues, but doing so for a symbolic matrix will just return a complicated expression for norm. Doable, but not very useful.
I understand that we're not allowed to change mpmath, but this idea does belong to mpmath.
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