Talk:Partial isometry

Explanation of reversion

I reverted the edits; the characterization given was incorrect:

Suppose W is a partial isometry. Then W W* is a self-adjoint projection, so that in particular

$e^2=e$

Also assume as was claimed in the previous edit, that any partial isometry satisfies:

$W=W^{*}W{W}^{*}$

Then multiply both sides by W:

$W^2=W{W}^{*}W{W}^{*}=e^2=e$

The square of a partial isometry is a projection only for very special partial isometries (it fails for instance for the unilateral shift). CSTAR 05:14, 9 Mar 2005 (UTC)