Re: [eigen] Problem inverting a Matrix4f with Eigen 2.0.0
• To: eigen@xxxxxxxxxxxxxxxxxxx
• Subject: Re: [eigen] Problem inverting a Matrix4f with Eigen 2.0.0
• Date: Sat, 17 Jul 2010 18:55:50 +0300

Hi Benoit,

Sorry, I meant the inverse in this sense, this is something that
arises when solving the two problems:

Ab = x
Ax = b

Where I leave the unknown as x, and the fixed as b.  Both problems can
be bound by a condition number that depends on the perturbations of x

\kappa = ||A||*||b||/||x||     <= ||A||*||A^-1|| (forward)
\kappa = ||A^-1||*||b||/||x|| <= ||A||*||A^-1|| (backward)

The term ||A||*||A^-1||, since it arises in both forward and backward
problems, is called the condition number of A.  This is pretty solidly
in the literature, and you wouldn't confuse anybody if you had a
general "calculate the condition number of a matrix" function and more
specialized ones for calculating the condition numbers of other
specific operations.

A



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