Currently, the default norm for matrices is the induced 2-norm, unless
the matrix is an RDF or CDF matrix, in which case the default norm is
the Frobenius norm. Needless to say, this is very confusing:
sage: a=matrix(QQ, 3, range(9))
sage: a.norm()
14.2267073908
sage: a.norm(2)
14.2267073908
sage: b=a.change_ring(RDF)
sage: b.norm()
14.2828568571
sage: b.norm('frob')
14.2828568571
It's particularly ironic since in order to calculate the (default)
induced 2-norm for QQ matrices, the first step is to change the matrix
to RDF/CDF and then calculate the 2-norm there.
Is there any objection to changing the default norm for RDF/CDF matrices
to the induced 2-norm? Of course, you can still get the Frobenius norm
by doing a.norm('frob').
This is ticket http://trac.sagemath.org/sage_trac/ticket/13643. I'll
post a patch there soon.
Thanks,
Jason
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