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Linear Algebra

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Moderate

Rotation No-Eigenvectors

LINALG-IXHKNE

The matrix:

$$R=\begin{pmatrix} \cfrac{\sqrt{2}}{2} & -\cfrac{\sqrt{2}}{2} \\\ \cfrac{\sqrt{2}}{2} & \cfrac{\sqrt{2}}{2}\end{pmatrix}$$

...is that corresponding to the linear transformation from:

$$\mathbb{R}^2\rightarrow\mathbb{R}^2$$

...which rotates vectors counter-clockwise by $\cfrac{\pi}{4}$ radians (i.e. $45$ degrees).

The eigenvalues of $R$ are:

A

$1$

B

$1$ and $-1$

C

$0$

D

Not real numbers