Talk:Polar decomposition

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[edit] Spectral decomposition when A is normal

It should surely be possible to say something about Λ and Q in terms of W, V and Σ. Can anybody give the relation? At the moment I can't quite see it. -- Jheald 02:49, 13 January 2006 (UTC).

Sorted. (I think). -- Jheald 11:50, 13 January 2006 (UTC).

[edit] a comment explaining revert

by the expression that A = UP, A is implicitly assumed to be square, since unitarity and positive semidefiniteness make sense only for square matrices. if A is not square, then a similar decomposition can probably be obtained, but U would then be weakened to a partial isometry or isometry (in the sense of matrices). it seems to me that only in the latter, mor general, case the comment that anon was adding would become necessary. Mct mht 03:19, 2 October 2006 (UTC)

Don't think this is true. The implication surely for a non-square A is that you can either zero-pad it, adding null rows or null columns; or (alternatively/equivalently) that U may non-square and span less than a full basis.

that's what is meant by an isometry or partial isometry (in the sense of matrices). Mct mht 14:49, 2 October 2006 (UTC)

Either way, there should be no problem in practice obtaining a polar decomposition for a non-square matrix. Jheald 12:06, 2 October 2006 (UTC).

that's what i said. what exactly is not true? Mct mht 14:49, 2 October 2006 (UTC)

[edit] Applications

It would be nice to read about applications. Anybody? CDaMama 16:56, 3 January 2007 (UTC)