A square matrix A is a special orthogonal matrix if A A^T = I, where I is the identity matrix, and the determinant satisfies det A = 1. The first condition means that A is an orthogonal matrix, and the second restricts the determinant to +1 (while a general orthogonal matrix may have determinant -1 or +1).

antisymmetric matrix | inner product | orthogonal group | orthogonal matrix | orthogonal transformation | special orthogonal group | unitary matrix