Lineare Algebra 2/Gemischte Satzabfrage/12/Aufgabe/Lösung

${\displaystyle {}V}$

${\displaystyle {}{\mathbb {K} }}$

${\displaystyle {}v_{1},v_{2},\ldots ,v_{n}}$

${\displaystyle {}V}$

${\displaystyle {}u_{1},u_{2},\ldots ,u_{n}}$

${\displaystyle {}V}$

${\displaystyle {}\langle v_{1},v_{2},\ldots ,v_{i}\rangle =\langle u_{1},u_{2},\ldots ,u_{i}\rangle \,}$

${\displaystyle {}i=1,\ldots ,n}$

${\displaystyle {}V\neq 0}$

${\displaystyle {}n}$

${\displaystyle [v_{1},\ldots ,v_{n}]\longmapsto [v_{1}\wedge \ldots \wedge v_{n}]}$

die Orientierungen

${\displaystyle {}V}$

${\displaystyle {}\bigwedge ^{n}V}$