Inner product
with linearity in the second argument, anti-linearity in the first, and positive definiteness with equality only at .
Inner products in $CC^n$
On the inner product is
It is Hermitian, ; linear in the second argument and anti-linear in the first, ; and positive definite, with equality iff . These axioms define an inner product on any vector space over or .
Related
Stated in
- Definition 2.10 (Real Inner Product)§2.2 Scalar Product (Dot Product)