An orthogonal matrix, or orthonormal matrix, is a square matrix whose columns and rows are orthonormal vectors.
Some examples of orthogonal matrices are rotation matrices and permutation matrices.
Orthogonal matrices imply orthogonal transformation. However, the converse is not true, as orthogonal transformations between spaces may be neither finite-dimensional nor of the same dimension, and these have no orthogonal matrix equivalent. 1
Properties of Orthogonal Matrices
- Inverse of a orthogonal matrix is its transpose
- Orthogonal Matrices Preserve Norm
- product of two orthogonal matrices is orthogonal