Editing Rotation (mathematics) (section)

====Further notes====
More generally, coordinate rotations in any dimension are represented by orthogonal matrices.  The set of all orthogonal matrices in {{mvar|n}} dimensions which describe proper rotations (determinant = +1), together with the operation of matrix multiplication, forms the [[special orthogonal group]] {{math|SO(''n'')}}.

Matrices are often used for doing transformations, especially when a large number of points are being transformed, as they are a direct representation of the [[Linear map|linear operator]]. Rotations represented in other ways are often converted to matrices before being used. They can be extended to represent rotations and transformations at the same time using [[homogeneous coordinates]]. [[Projective transformation]]s are represented by {{gaps|4|×|4}} matrices. They are not rotation matrices, but a transformation that represents a Euclidean rotation has a {{gaps|3|×|3}} rotation matrix in the upper left corner.

The main disadvantage of matrices is that they are more expensive to calculate and do calculations with. Also in calculations where [[numerical stability|numerical instability]] is a concern matrices can be more prone to it, so calculations to restore [[orthonormality]], which are expensive to do for matrices, need to be done more often.