Unformatted text preview: −→ ∇ g ( −→ u ) = 2 −→ u ; we need to calculate −→ ∇ f ( −→ u ). To this end, we write f ( x 1 ,x 2 ,x 3 ) = Q ( x 1 ,x 2 ,x 3 ) in the matrix form f ( x 1 ,x 2 ,x 3 ) = b x 1 x 2 x 3 B a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 x 1 x 2 x 3 = 3 s i =1 3 s j =1 a ij x i x j . To ±nd ∂f ∂x 1 , we locate all the terms involving x 1 : they are a 11 x 2 1 + a 12 x 1 x 2 + a 13 x 1 x 3 + a 21 x 2 x 1 + a 31 x 3 x 1 ; using the symmetry of A we can combine some of these terms to get a 11 x 2 1 + 2 a 12 x 1 x 2 + 2 a 13 x 1 x 3 . 19 we return to the negative defnite case at the end oF this subsection...
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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, Determinant

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