University Mathematics Handbook (2015)
X. Algebra
Chapter 12. Quadratic Form
a. The expression , when is a symmetric matrix in and is called quadratic form.
b. Example in :
A quadratic form is positive (non-negative) if for every
,
c. A quadratic form is negative (non-positive) if for every , .
d. The following propositions are equivalent
1. Quadratic form is positive.
2. The eigenvalues of are positive.
3. All numbers
,…..,detA (*)
are positive.
e. Quadratic form is negative if and only if the signs of the n numbers in (*) change intermittently, the first being negative.