Find the standard inner product on P^2 of the given polynomials p=−5+4x+x^2,q=3+4x–2x^2.

Question
Matrix transformations
asked 2020-11-20
Find the standard inner product on \(\displaystyle{P}^{{2}}\) of the given polynomials \(\displaystyle{p}=−{5}+{4}{x}+{x}^{{2}},{q}={3}+{4}{x}–{2}{x}^{{2}}\).

Answers (1)

2020-11-21
On \(\displaystyle{P}^{{2}}\) the standart inner product is given by, for \(\displaystyle{p}{\left({x}\right)}={a}{0}+{a}{1}{x}+{a}{2}{x}^{{2}},{q}{\left({x}\right)}={b}{0}+{b}{1}{x}+{b}{2}{x}^{{2}}∈{P}^{{2}}\).
PSK(p,q)=a0b0+a1b1x+a2b2x^2 =-5*3+4*4x+(-2)x^2 =-15+16x-2x^2ZSK
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