線型方程式系
[ a 11 a 12 k a 11 k a 12 ] [ x 1 x 2 ] = [ b 1 b 2 ] , k = a 11 ̄ a 21 + a 12 ̄ a 22 | a 11 | 2 + | a 12 | 2 {\displaystyle {\begin{bmatrix}a_{11}&a_{12}\\ka_{11}&ka_{12}\end{bmatrix}}{\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}}={\begin{bmatrix}b_{1}\\b_{2}\end{bmatrix}},\quad k={\frac {{\overline {a_{11}}}a_{21}+{\overline {a_{12}}}a_{22}}{|a_{11}|^{2}+|a_{12}|^{2}}}}
と書けて、 b 2 ≠ k b 1 {\displaystyle b_{2}\neq kb_{1}} のとき解なし。 b 2 = k b 1 {\displaystyle b_{2}=kb_{1}} のとき