Gegeben seien im euklidische Vektorraum (P≤2,⟨ , ⟩)\left(\mathcal P_{\leq 2}, \langle \ , \ \rangle \right)(P≤2,⟨ , ⟩) mit ⟨p,q⟩=∫−11p(x)q(x) dx\displaystyle \langle p, q \rangle = \int_{-1}^{1} p(x)q(x) \; dx⟨p,q⟩=∫−11p(x)q(x)dx
(P≤2,⟨ , ⟩)\left(\mathcal P_{\leq 2}, \langle \ , \ \rangle \right)(P≤2,⟨ , ⟩)
⟨p,q⟩=∫−11p(x)q(x) dx\displaystyle \langle p, q \rangle = \int_{-1}^{1} p(x)q(x) \; dx⟨p,q⟩=∫−11p(x)q(x)dx
die Polynome p, q :[−1,1]→R{\color{red}p}, \ {\color{blue}q} \; : [-1,1] \to \mathbb Rp, q:[−1,1]→R mit p(x)=4x2+5x+5{\color{red}p(x) = 4x^2 + 5x +5}p(x)=4x2+5x+5 und q(x)=dx+1q(x) = {\color{blue}d}x + 1q(x)=dx+1.
p, q :[−1,1]→R{\color{red}p}, \ {\color{blue}q} \; : [-1,1] \to \mathbb Rp, q:[−1,1]→R
p(x)=4x2+5x+5{\color{red}p(x) = 4x^2 + 5x +5}p(x)=4x2+5x+5
q(x)=dx+1q(x) = {\color{blue}d}x + 1q(x)=dx+1
Für welches d{\color{blue}d}d stehen p{\color{red}p}p und q{\color{blue}q}q senkrecht aufeinander?
d{\color{blue}d}d
p{\color{red}p}p
q{\color{blue}q}q
d={\color{blue}d} =d=