Week of 1/21/08
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<math>h(z,w) \equiv \sum z_i w^* _i</math> | <math>h(z,w) \equiv \sum z_i w^* _i</math> | ||
− | NB if <math>z = x + I y</math>, then <math>z^* z = (x - I y)(x + I y) = x^2 + y^2 = z z^*</math> | + | |
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+ | '''NB''' if <math>z = x + I y</math>, then <math>z^* z = (x - I y)(x + I y) = x^2 + y^2 = z z^*</math> |
Revision as of 15:38, 21 January 2008
Definition of complex (Hermitian) inner product
It's a matter of convention that the anti-linear term is the second one in the inner product:
with equality only if
The basic example is the form
NB if z = x + Iy, then z * z = (x − Iy)(x + Iy) = x2 + y2 = zz *