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Unformatted text preview: u 1 P = u 1 = { x R 3  x u = 0 } and look at the restriction of Q to the circle P S 2 = { u R 3  u u 1 = 0 and u u = 1 } . This has a minimum at u 2 and a maximum at u 3 , each of which is a solution of the Lagrange multiplier equations f ( u ) = g 1 ( u ) + g 2 ( u ) g 1 ( u ) = u u = 1 g 2 ( u ) = u u 1 = 0 . Again, we have, for i = 1 , 2 , 3, f ( u ) = 2 A u g 1 ( u ) = 2 u 20 Another terminology calls an eigenvector a characteristic vector and an eigenvalue a characteristic value of A ....
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 Spring '08
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 Calculus, Scalar

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