Positive definite
Let
K be the
field R or
C,
V is a
vector space over
K, and
B :
V ×
V →
K is a
bilinear map which is Hermitian in the sense that
B(
x,
y) is always the complex conjugate of
B(
y,
x). Then
B is
positive-definite if
B(
x,
x) > 0 for every nonzero
x in
V.
A self-adjoint operator A on an inner product space is positive-definite if (x, Ax) > 0 for every nonzero vector x.
See in particular positive-definite matrix.