Inner
Product
§Inner Product: Let V be a vector space over C. An inner product on V is a complex valued
function, <·, ·>: V ´ V ® C
Such
that for any x, y, z ÎV and a, bÎC
(i) <x, ay+bz>=a<x,y>+b<x,z>
(ii) <x,y>=<y,z>*
(complex conjugate)
(iii) <x,x> >0 if x¹ 0.
§Inner product on Cn:
x and y are orthogonal if Ð (x,y)= ½p
