An unfamiliar inner product

by Ancient Tree·

Consider $E=\mathcal{F}(\R)$ the space of real functions $f:\R \rightarrow \R$ .

Let’s define :
$\langle f, g\rangle=f g$ Is $\langle,\rangle$ an inner product ?

I solved itMark it done Add to my listKeep it in your list

I like this problem3 likes

Liked by

Sequoia@sequoia
NawzadHogan@nawzadhogan
darktoaster@darktoaster

Solutions

Reveal solutionsAre you sure? Give it a try first.

Solution by Ancient Tree

Discussions1 useful vote

This is a trick question. All the properties of an inner product seem to be satisfied : it is bilinear, symmetric, and seemingly positive definite. However, an inner product is with values in $\R$ , whereas $\langle f,g \rangle$ is a function.

Report