Unformatted text preview: of Q . If Δ 2 > 0, then Q is defnite , which is to say the two coe±cients in the expression for Q ( x 1 ,x 2 ) have the same sign; to tell whether it is positive deFnite or negative deFnite, we need to decide if this sign is positive or negative, and this is most easily seen by looking at the sign of a , which we will denote Δ 1 . The signiFcance of this notation will become clear later. With this notation, we have Proposition 3.8.5. A quadratic Form Q ( x 1 ,x 2 ) = ax 2 1 + 2 bx 1 x 2 + cx 2 2 16 Note that if either coeFcient is zero, then there is a whole line along which Q = 0, so it is not de±nite....
View
Full Document
 Fall '08
 ALL
 Calculus, Linear Algebra, Negative and nonnegative numbers, Quadratic form

Click to edit the document details