# "기저와 선형결합"의 두 판 사이의 차이

둘러보기로 가기 검색하러 가기

##### 예

$$v(1)=\{1, 0\}$$

$$v(2)=\{-(\sqrt{3}/2), 1/2\}$$

$$\begin{array}{|rcl|} \hline \{1,0\} & = & v(1) \\ \hline \left\{\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & \sqrt{3} v(1)+v(2) \\ \hline \left\{\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & 2 v(1)+\sqrt{3} v(2) \\ \hline \{0,1\} & = & \sqrt{3} v(1)+2 v(2) \\ \hline \left\{-\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & v(1)+\sqrt{3} v(2) \\ \hline \left\{-\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & v(2) \\ \hline \{-1,0\} & = & -v(1) \\ \hline \left\{-\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -\sqrt{3} v(1)-v(2) \\ \hline \left\{-\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -2 v(1)-\sqrt{3} v(2) \\ \hline \{0,-1\} & = & -\sqrt{3} v(1)-2 v(2) \\ \hline \left\{\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -v(1)-\sqrt{3} v(2) \\ \hline \left\{\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -v(2) \\ \hline \end{array}$$

$$\begin{array}{|rcl|} \hline \{1,0\} & = & v_1 \\ \hline \left\{\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & \sqrt{3} v_1+v_2 \\ \hline \left\{\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & 2 v_1+\sqrt{3} v_2 \\ \hline \{0,1\} & = & \sqrt{3} v_1+2 v_2 \\ \hline \left\{-\frac{1}{2},\frac{\sqrt{3}}{2}\right\} & = & v_1+\sqrt{3} v_2 \\ \hline \left\{-\frac{\sqrt{3}}{2},\frac{1}{2}\right\} & = & v_2 \\ \hline \{-1,0\} & = & -v_1 \\ \hline \left\{-\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -\sqrt{3} v_1-v_2 \\ \hline \left\{-\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -2 v_1-\sqrt{3} v_2 \\ \hline \{0,-1\} & = & -\sqrt{3} v_1-2 v_2 \\ \hline \left\{\frac{1}{2},-\frac{\sqrt{3}}{2}\right\} & = & -v_1-\sqrt{3} v_2 \\ \hline \left\{\frac{\sqrt{3}}{2},-\frac{1}{2}\right\} & = & -v_2 \\ \hline \end{array}$$

• 도서내검색