Dann mal ein Hinweis zu Gram-Schmitt
Text erkannt (test) :
\( \rightarrow \mathbf{e} \mathbf{1}:=\{\mathbf{1}, \mathbf{1},-\mathbf{1}, \mathbf{2}\} \)
\( o1:=\mathrm{e} 1 / c b etrag(\mathrm{e} 1) \)
\( \rightarrow \) o1 \( :=\left\{\frac{1}{\sqrt{7}}, \frac{1}{\sqrt{7}},-\frac{1}{\sqrt{7}}, \frac{2}{\sqrt{7}}\right\} \)
\( \rightarrow \mathbf{e} 2:=\{\mathbf{1},-\mathbf{1}, \mathbf{1}, \mathbf{2}\} \)
\( \mathrm{c} 2:=\mathrm{e} 2-\mathrm{cdot} (\mathrm{e} 2,o1)^{\mathrm{x}} \mathrm{o} 1 \)
\( \rightarrow \quad \mathrm{c} 2:=\left\{\frac{4}{7},-\frac{10}{7}, \frac{10}{7}, \frac{8}{7}\right\} \)
\( o2:=c 2 / c b etrag(c 2) \)
\( \rightarrow \) \( o2:=\left\{\frac{1}{35} \sqrt{70},-\frac{1}{14} \sqrt{70}, \frac{1}{14} \sqrt{70}, \frac{2}{35} \sqrt{70}\right\} \)
\( \rightarrow \mathbf{e} 3:=\{2, \mathbf{1}, \mathbf{1}, \mathbf{4}\} \)
\( \mathrm{c} 3:=\mathrm{e} 3-\mathrm{cdot}(\mathrm{e} 3, \mathrm{o} 2) \mathrm{o} 2-\mathrm{cdot}(\mathrm{e} 3, \mathrm{o} 1) \mathrm{o} 1 \)
\( \rightarrow \mathbf{c} 3:=\{\mathbf{0}, \mathbf{1}, \mathbf{1}, \mathbf{0}\} \)
\(o 3:= \) Simplify \( (c 3 / cbetrag (\mathrm{c} 3)) \)
\( \rightarrow \mathbf{o} \mathbf{3}:=\left\{\mathbf{0}, \frac{\mathbf{1}}{\sqrt{2}}, \frac{\mathbf{1}}{\sqrt{2}}, \mathbf{0}\right\} \)
\( \{\operatorname{cdot}(o1,o2), \operatorname{cdot} (o1,o3), \operatorname{cdot} (o2,o3)\} \)
\( \rightarrow\{\mathbf{0}, \mathbf{0}, \mathbf{0}\} \)