Talk:Orthogonal complement

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[edit] Vacuously true?

"In infinite-dimensional Hilbert spaces, it is of some interest to observe that every orthogonal complement is closed in the metric topology—a statement that is vacuously true in the finite-dimensional case."

Why is this vacuously true? For instance, in R⁴, isn't the orthogonal complement of the vector subspace generated by (1,0,0,0) and (0,1,0,0) the vector subspace generated by (0,0,1,0) and (0,0,0,1), which is closed in the metric topology? It's a little trivial since all vector subspaces are closed in the finite case, but it's not vacuously true, which would imply there are no orthogonal complements.--Syd Henderson 05:49, 16 February 2007 (UTC)

You're right, it's not vacuously true (although it can be reformulated so that it is). Anyway, I've reworded the sentence to make it more general, and removed the "vacuously true" claim. --Zundark 13:38, 16 February 2007 (UTC)

[edit] <x|y>

In the equation following "orthogonal to every vector in W, i.e., it is"...what does <x|y> represent ? 59.93.48.101 07:44, 20 May 2007 (UTC)sridhar email id: sridhar10chitta@yahoo.com59.93.48.101 07:44, 20 May 2007 (UTC)

It's the inner product, in bra-ket notation. I've changed it to use the same notation as the inner product space article. --Zundark 08:17, 20 May 2007 (UTC)