(b) On R2, the function (v, w) =v1W1+vịw2+v2w1+ V2W2. %3D

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Introduction:

A dot product $(v,w)$ is called an inner product, when it follows the below three axioms:

(i) Linearity: $\left(au+bv,w\right)=a(u,w)+b(v,w)$

(ii) symmetric $\left(v,w\right)=(w,v)$

(iii) Positive definite: For any $v\in V$, $\left(v,v\right)\ge 0$ and $\left(v,v\right)=0$ if and only if $v=0$.