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:


 * $$ W = W^* W W^* \quad $$

Then multiply both sides by W:


 * $$ W^2 = W W^* W W^* = e^2 = e \quad $$

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)