It is possible to use the SVD of a square matrix to determine the orthogonal matrix closest to . The closeness of fit is measured by the Frobenius norm of . The solution is the product . This intuitively makes sense because an orthogonal matrix would have the decomposition where is the identity matrix, so that if then the product amounts to replacing the singular values with ones. Equivalently, the solution is the unitary matrix of the Polar Decomposition in either order of stretch and rotation, as described above.