Hermitian inner product

Hermitian inner product

[er′mish·ən ′in·ər ¦präd·əkt]
(mathematics)
Mentioned in ?
References in periodicals archive ?
Recall that Hermitian inner product is denoted and calculated by [<u, v).sub.H] = [[summation].sup.n-1.sub.i=0] [u.sub.i][THETA]([v.sub.i]), for all u = ([u.sub.0], ..., [u.sub.n-1]) and v = ([v.sub.0], ..., [v.sub.n-1]) in [mathematical expression not reproducible].
The Hermitian inner product is defined only when the order of [THETA] is 2.
The standard Hermitian inner product of two complex vectors u, v [member of] [C.sup.N] is defined as
The Hermitian inner product of X, Y [member of] [F.sup.n.sub.4] is defined as
If [mathematical expression not reproducible] and [rho](a) = [a.sup.q] (resp., [rho](a + ub) = [a.sup.q] + [ub.sup.q]) for all a [member of] [mathematical expression not reproducible], the [rho]-inner product is called the Hermitian inner product and denoted by [<u, v>.sub.H].