## Elementary Linear Algebra 7th Edition

Let $f(x)= x, g(x)=\frac{1}{2}(5x^3-3x)$, $C[-1,1]$ \begin{aligned}\langle f,g\rangle &=\int_{-1}^{1}\frac{1}{2}(5x^4-3x^2) d x\\ &=\left[\frac{1}{2}( x^5- x^3) \right]_{-1}^{1} \\ &=0 \end{aligned}. then $f$ and $g$ are orthogonal in the inner product space $C[-1,1]$.