# The Matrix of a Rotation

by Roger C. Alperin (San Jose State University)

College Mathematics Journal
May, 1989

Subject classification(s): Algebra and Number Theory | Linear Algebra | Eigenvalues and Eigenvectors | Linear Transformations | Vectors in R3 | Geometry and Topology | Plane Geometry | Angles | Lines and Planes
Applicable Course(s): 3.8 Linear/Matrix Algebra | 4.14 Vector Analysis

Given a unit vector $p$ in $\mathbf{R}^3$ and an angle $\theta$, what is the matrix of the rotation of $\mathbf{R}^3$ about $p$ through an angle of $\theta$ in terms of the standard basis?  The author obtains an explicit matrix without changing bases.

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