A.11. Square Root of a Symmetric Nonnegative Definite Matrix

For a symmetric nonnegative definite matrix (that is, all eigenvalues of the matrix are nonnegative), A, one can find an upper triangular matrix U such that A = U'U. This is called the Cholesky decomposition. The function ROOT can find this matrix U. The corresponding SAS statement is

u = root(a);

For the symmetric nonnegative definite (since its eigenvalues were found to be nonnegative) matrix, SYM defined earlier, we can compute U as