\(w=\sum\limits_{j=1}^{n}cdot\left(o_j, u \right) o_j \)
\(\small \text{w ∈ Spann ONB=}\)\(\left(o_1, . . , o_n\right) \quad \text{Vektor mit dem kleinsten Abstand } |u-ONB_U|\)
$$ONB_{U} \, := \, \left(\begin{array}{rrr}\frac{1}{\sqrt{3}}&\frac{-1}{\sqrt{6}}&\frac{-1}{\sqrt{2}}\\\frac{1}{\sqrt{3}}&\frac{2}{\sqrt{6}}&0\\0&0&0\\\frac{1}{\sqrt{3}}&\frac{-1}{\sqrt{6}}&\frac{1}{\sqrt{2}}\\\end{array}\right)$$
===>
\(w=\left(\begin{array}{r}0\\1\\0\\0\\\end{array}\right)\)
oder
U: x3=0 , n={0,0,1,0}T
w:=u - cdot(u, n) n
