Rotation matrix

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In linear algebra, a rotation matrix is a transformation matrix
that is used to perform a rotation in Euclidean space.

Rotation matrices are square matrices, with real entries.
More specifically, they can be characterized as orthogonal matrices with determinant 1;
that is, a square matrix R is a rotation matrix if and only if RT = R−1 and det R = 1.

The set of all orthogonal matrices of size n with determinant +1 forms a group
known as the special orthogonal group SO(n),
one example of which is the rotation group SO(3).
The set of all orthogonal matrices of size n with determinant +1 or −1
forms the (general) orthogonal group O(n).