This preview shows page 1. Sign up to view the full content.
Unformatted text preview: + is unchanged. Thus, any other matrix with the same diagonal entries and , and whose odiagonal entries add up to + , leads to the same function Q ( x,y ). To standardize things, we require that the matrix be symmetric. This amounts to balancing the two mixed product terms: each is equal to half will have some useful consequences down the road. Thus the matrix representative of a quadratic form Q ( x,y ) in two variables is the symmetric 2 2 matrix [ Q ] satisfying Q ( x ) = [ x ] T [ Q ][ x ] . (3.30) You should conFrm that this is the same as the matrix representative we used in 3.8 . When we apply Equation ( 3.30 ) to a quadratic form in three variables Q ( x 1 ,x 2 ,x 3 ), we get a symmetric 3 3 matrix. The diagonal entries of [ Q ]...
View Full
Document
 Spring '08
 ALL
 Calculus

Click to edit the document details