Practicing Success
If $A = \begin{bmatrix} \cos α & \sin α\\ -\sin α & \cos α \end{bmatrix}$, then : |
A'A = I A'A = 0 A'A = 2I A'A = -I |
A'A = I |
$A = \begin{bmatrix} \cos α & \sin α\\ -\sin α & \cos α \end{bmatrix}$ $A' = \begin{bmatrix} \cos α & -\sin α\\ \sin α & \cos α \end{bmatrix}$ So $AA' = \begin{bmatrix} \cos α & \sin α\\ -\sin α & \cos α \end{bmatrix} \begin{bmatrix} \cos α & -\sin α\\ \sin α & \cos α \end{bmatrix}$ $AA' = \begin{bmatrix} \cos^2 α + \sin^2 α & -\cos α \sin α + \cos α \sin α\\ -\cos α \sin α + \cos α \sin α & \cos^2α + \sin^2α \end{bmatrix}$ $= \begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix} = I$ |