[Numpy-discussion] Inaccuracy in documentation of np.linalg.pinv
Hao Xiong
hao at biostat.ucsf.edu
Tue Mar 8 20:01:50 EST 2011
I think the documentation for np.linalg.pinv contains some inaccuracies.
Most importantly, Moore-Penrose is not defined by the solution to the
least-square
problem. It was defined by the unique solution to 4 equations. Since SVD
can be easily shown to satisfy the same 4 equations, it is the
Moore-Penrose inverse.
Another way that definition is wrong is that the least-square problem
does not have to have
unique solution. In fact, it can have infinitely many. In this case,
Moore-Penrose is the minimum
norm solution.
All of this is discussed in the Matlab documentation of pinv, which is
very good.
Hao
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