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Calculus and Beyond Homework Help
Proving that the orthogonal subspace is invariant
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[QUOTE="Dixanadu, post: 4533764, member: 451060"] Hi guys, I couldn't fit it all into the title, so here's what I'm trying to do. Basically, I have a unitary representation [itex]V[/itex]. There is a subspace of this, [itex]W[/itex], which is invariant if I act on it with any map [itex]D(g)[/itex]. How do I prove that the orthogonal subspace [itex]W^{\bot}[/itex] is also an invariant subspace of [itex]V[/itex]? I know that an orthogonal matrix is one where its transpose is its own inverse, but I don't know how to apply that here. Can you guys help me out? thanks! [/QUOTE]
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Proving that the orthogonal subspace is invariant
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