be the field R
is a vector space
, and B
is a bilinear
map which is Hermitian in the sense that B
) is always the complex conjugate of B
). Then B
) > 0 for every nonzero x
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.