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matrix norm

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orkolorko
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matrix norm

Fri Mar 01, 2013 1:03 pm
Hi,
I'm sorry to disturb, but I would like to ask how the lp norms are computed when dealing with matrices?

If we take the usual mathematical definition of:
||A||=\sup_{||v||=1}||Av||

then ||A||=\max ||A e_i||, but it does not seem to me that eigen implements this norm.

I tried to implement it using colwise reduction, but

(A.colwise()).lpNorm<1>()
is not defined (A is dense).

Bests
Isaia
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ggael
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Re: matrix norm

Fri Mar 01, 2013 1:14 pm
As explain in the doc (http://eigen.tuxfamily.org/dox-devel/cl ... 84371188bf) lpNorm on a matrix works just like all entries would form a single vector. This corresponds to the class of "entry -wise" norms (http://en.wikipedia.org/wiki/Matrix_nor ... e.22_norms).


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