Engineering Calculus Notes 398

Engineering Calculus Notes 398 - [ Q ] = 1 1 1 and it is...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
386 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION from which we easily get the following test for a quadratic form in three variables to be negative deFnite: Corollary 3.9.7 (Determinant Test for Negative DeFnite ±orms in R 3 ) . The quadratic form Q in three variables is negative deFnite precisely if its matrix representative A = [ Q ] satisFes ( 1) k Δ k > 0 for k = 1 , 2 , 3 where Δ k are the determinants given in Proposition 3.9.6 . Let us see how this test works on the examples studied in detail earlier in this section. 1. The form Q ( x,y,z ) = x 2 y 2 z 2 has matrix representative
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: [ Q ] = 1 1 1 and it is easy to calculate that 1 = det[ Q ] = (1)( 1)( 1) = 1 > ...which, so far, tells us that the form is not negative deFnite. .. 2 = (1)( 1) = 1 < so that Q is also not positive deFnite. There is no further information to be gained from calculating 1 = 1 . 2. The form Q ( x,y,z ) = 2 xy + 2 xz + 2 yz has matrix representative [ Q ] = 0 1 1 1 0 1 1 1 0...
View Full Document

Ask a homework question - tutors are online