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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.
See also:
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