Thread: Let p and q be polynomials of degree R[x].Define

<p,q> =p(xo)q(xo) + p(x1)q(x1) + ….. + p(xn)q(xn) ,where x0,x1,…xn are distinct real numbers.
Check whether or not <,> defines an inner product on pn(R).

Originally Posted by puneet

<p,q> =p(xo)q(xo) + p(x1)q(x1) + ….. + p(xn)q(xn) ,where x0,x1,…xn are distinct real numbers.
Check whether or not <,> defines an inner product on pn(R).

Check these properties of the inner product :

• <p,q> = <q,p>
• <λp,q> = λ<p,q> (λ ∈ ℝ)
• <p,p> = 0 <=> p=0