Concept

# Rotation matrix

Summary
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix :R = \begin{bmatrix} \cos \theta & -\sin \theta \
\sin \theta & \cos \theta \end{bmatrix}
rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R:

# : R\mathbf{v} = \begin{bmatrix} \cos \theta & -\sin \theta \\sin \theta & \cos \theta \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix}

\begin{bmatrix} x\cos\theta-y\sin\theta \ x\sin\theta+y\cos\theta \end{bmatrix}. If x and y are the endpoint coordinates of a vector, where x is cosine and y is sine, then the
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