Unformatted text preview: y  2 +  xy  2 = 2  x  2 + 2  y  2 5. If U is a subspace of R n of dimension k , then prove that dim U ⊥ = nk . Hint: use Theorem 3 from Chapter 6, The Rank Theorem (Theorem 14 from Chapter 2) and the fact that for any matrix rankA = rankA T . 6. If A is an n × n complex matrix then prove that ( A H x ) · y = x · ( A y ) for all x , y ∈ C n . 1...
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 Fall '08
 CELMIN
 Math, Linear Algebra, Algebra, #, Complex number, Rn of dimension, Compute quantities

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