Talk:Partial isometry

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[edit] 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

e2 = 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)