Unformatted text preview: âˆ’â†’ u 1 P = âˆ’â†’ u âŠ¥ 1 = { âˆ’â†’ x âˆˆ R 3  âˆ’â†’ x Â· âˆ’â†’ u = 0 } and look at the restriction of Q to the circle P âˆ© S 2 = { âˆ’â†’ u âˆˆ R 3  âˆ’â†’ u Â· âˆ’â†’ u 1 = 0 and âˆ’â†’ u Â· âˆ’â†’ u = 1 } . This has a minimum at âˆ’â†’ u 2 and a maximum at âˆ’â†’ u 3 , each of which is a solution of the Lagrange multiplier equations âˆ’â†’ âˆ‡ f ( âˆ’â†’ u ) = Î» âˆ’â†’ âˆ‡ g 1 ( âˆ’â†’ u ) + Î¼ âˆ’â†’ âˆ‡ g 2 ( âˆ’â†’ u ) g 1 ( âˆ’â†’ u ) = âˆ’â†’ u Â· âˆ’â†’ u = 1 g 2 ( âˆ’â†’ u ) = âˆ’â†’ u Â· âˆ’â†’ u 1 = 0 . Again, we have, for i = 1 , 2 , 3, âˆ’â†’ âˆ‡ f ( âˆ’â†’ u ) = 2 A âˆ’â†’ u âˆ’â†’ âˆ‡ g 1 ( âˆ’â†’ u ) = 2 âˆ’â†’ u 20 Another terminology calls an eigenvector a characteristic vector and an eigenvalue a characteristic value of A ....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus, Scalar

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