# Tag Info

An inner product is a map from a vector space crossed with itself to $\mathbb{R}$ or $\mathbb{C}$. Also an inner product must be positive definite: $\langle x, x\rangle\geq 0$. A bilinear map, to contrast, is simply a map $A\times B\to C$ for linear spaces $A,B,C$ which is bilinear. I think positive definiteness is the most important thing that inner ...