Unformatted text preview: Proj U : V → U of V onto U . b. if { u 1 ,...,u m } is an orthonormal basis of U , and { v 1 ,...,v n } is an orthonormal basis of U ⊥ , prove that { u 1 ,...,u m ,v 1 ,...,v n } is orthonormal, and that it’s a basis of V . c. since U ⊂ V , Proj U is also an operator on V . prove a basis from part b is always a basis of eigenvectors of Proj U : V → V . 1...
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 Spring '11
 Carlsson
 Linear Algebra, Algebra, #, Hilbert space, Orthonormal basis, Vladimir

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