Inner product space
= Inner product space
{title2=$(V,\langle\cdot,\cdot\rangle)$}
{wiki}
An inner product space is a real or complex <vector space> equipped with a positive-definite <inner product>. Over the real numbers the form is symmetric and bilinear; over the complex numbers it is conjugate symmetric and sesquilinear. It defines the <norm> $\|v\|=\sqrt{\langle v,v\rangle}$. The <Cauchy-Schwarz inequality> proves the triangle inequality for this norm. A complete inner product space is a <Hilbert space>; every finite-dimensional inner product space is complete.