Comment #14 on issue 2225 by [email protected]: Enhancing Matrix Norm
http://code.google.com/p/sympy/issues/detail?id=2225
I e-mailed this to the list, it doesn't appear to be coming up. I apologize
if a repeat post happens.
Example:
Spectral norm of a matrix (standard 2-norm) can be defined as the largest
singular value of that matrix. This is the maximum amount that the matrix
can "grow" the 2-norm of a vector.
We can define the principal singular value of a matrix A as the square root
of the largest eigenvalue of (A.T * A) (real).
We have symbolic methods to compute eigenvalues (you learned them briefly
in high school) so this is alright so far.
The issue I'm having is that I need to return the largest of the
eigenvalues and I don't know apriori which that is if things are symbollic.
Ideally (I think) I'd return some sort of "Max" object like how we deal
with Adds and Pows.
consider A = Matrix([[1 0], [0, x]])
norm(A) == max(1,x) #I'm not sure which it should be yet. We can decide
once we have a value for x.
sherjilo... you're right that they end up coming out as very complicated
expressions. For even very simple matrices they're often hideous.
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