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Talk:Partial isometry

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Explanation of reversion

[edit]

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

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

Then multiply both sides by W:

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)