Question

the matrix of the qudratic form
$x {}^{2} + y {}^{2} + z {}^{2}$
​

Answer 1

Theorem 1 Any quadratic form can be represented by symmetric matrix. ... The quadratic form Q(x, y) = x2 + y2 is positive for all nonzero (that is (x, y) = (0,0)) arguments (x, y). Such forms are called positive definite. The quadratic form Q(x, y) = −x2 − y2 is negative for all nonzero argu- ments (x, y)