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Unformatted text preview: k k 2 = k ~v 1 k 2 + + k ~v k k 2 4. Let V be a nite dimensional inner product space. Let L : V V be a linear operator. (a) If B = { ~v 1 ,...,~v n } is an orthonormal basis for V , then prove that the ijth entry of [ L ] B is h L ( ~v j ) ,~v i i . (b) Prove that if h ~v,L ( ~w ) i = h L ( ~v ) , ~w i for all ~v, ~w V , then for any orthonormal basis C of V , we have that [ L ] C is symmetric (that is, ([ L ] C ) ij = ([ L ] C ) ji )....
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 Spring '08
 CELMIN
 Math

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