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Math Help - Let p and q be polynomials of degree R[x].Define

  1. #1
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    Post 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).
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    Quote Originally Posted by puneet View Post
    <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
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