Definite bilinear form
- B(v, v)
has a fixed sign (positive or negative) when it is not 0.
- B : V × V → K
- B(x, x) > 0
for every nonzero x in V. If it is greater than or equal to zero, we say B is positive semidefinite. Similarly for negative definite and negative semidefinite. If it is otherwise unconstrained, we say B is indefinite.
- (x, Ax) > 0 for every nonzero vector x.
See in particular positive-definite matrix.