Untervektorraum/Durchschnitt/Dimensionsabschätzung/Fakt/Beweis

Beweis

Nach Fakt ist

{}{\begin{aligned}\operatorname {dim} _{}\left(U_{1}\cap U_{2}\right)&=\operatorname {dim} _{}\left(U_{1}\right)+\operatorname {dim} _{}\left(U_{2}\right)-\operatorname {dim} _{}\left(U_{1}+U_{2}\right)\\&=n-k_{1}+n-k_{2}-\operatorname {dim} _{}\left(U_{1}+U_{2}\right)\\&\geq n-k_{1}+n-k_{2}-n\\&=n-k_{1}-k_{2}.\end{aligned}}

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