In Euclidean spaces of n dimensions, this operation is represented by the special orthogonal group of order n. Along with translations and boosts, operations of this kind make up the Lorentz group of special relativity. In quantum mechanics, the angular momentum operator is the generator of the infinitesimal operations of this kind. The plane of polarization will undergo this action in light propagating along a magnetic field, and for a rigid body, any action of this type can be decomposed into three actions of this kind performed with respect to the Euler angles. In two dimensions, performing this operation by some angle theta involves multiplying by a matrix whose four entries are cosine-theta, sine-theta, minus-sine-theta, and cosine-theta. For 10 points, identify this operation which involves displacing an obj
In Euclidean spaces of n dimensions, this operation is represented by the special orthogonal group of order n. Along with translations and boosts, operations of this kind make up the Lorentz group of special relativity. In quantum mechanics, the angular momentum operator is the generator of the infinitesimal operations of this kind. The plane of polarization will undergo this action in light propagating along a magnetic field, and for a rigid body, any action of this type can be decomposed into three actions of this kind performed with respect to the Euler angles. In two dimensions, performing this operation by some angle theta involves multiplying by a matrix whose four entries are cosine-theta, sine-theta, minus-sine-theta, and cosine-theta. For 10 points, identify this operation which involves displacing an object along an angular, rather than a linear coordinate.
In Euclidean spaces of n dimensions, this operation is represented by the special orthogonal group of order
rotation