Angle under an orthogonal map

EasyLinear Algebra~3m

Vectors $x, y \in \mathbb{R}^n$ have an angle of $75^\circ$ between them. If $A$ is an $n \times n$ orthogonal matrix, what is the angle (in degrees) between $Ax$ and $Ay$ ?

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Orthogonal means $A^\top A = I$ . What does that do to $\langle Ax, Ay\rangle$ ?
Inner products (and lengths) are preserved, so the angle is unchanged.

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Asked at: Citadel, Two Sigma

Angle under an orthogonal map

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