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The Matrix of a Rotation

by Roger C. Alperin (San Jose State University)

This article originally appeared in:
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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Capsule Course Topic(s):
Linear Algebra | Linear Transformation
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