A n×n matrix A is an orthogonal matrix if A A^T = I, where A^T is the transpose of A and I is the identity matrix. In particular, an orthogonal matrix is always invertible, and A^(-1) = A^T. In component form, (a^(-1))_(i j) = a_(j i). This relation make orthogonal matrices particularly easy to compute with, since the transpose operation is much simpler than computing an inverse.

antisymmetric matrix | Euler's rotation theorem | improper rotation | inner product | orthogonal group | orthogonality condition | orthogonal transformation | orthonormal basis | rotation | rotation matrix | special orthogonal matrix | symmetric matrix | unitary matrix