7 Symmetric Matrices 7 Symmetric Matrices 7.2 LU Decomposition of Symmetric Matrices

7.1 LDU Decomposition of Symmetric Matrices

If A is symmetric, its LDU decomposition is symmetric, i.e.

\mathbf{L={U}^{T}}

(74)

and

\mathbf{U={L}^{T}}

(75)

For this reason, the LDU decomposition of a symmetric matrix is sometimes referred to as an LDL^T decomposition. The elements L and U of the LDU decomposition of a symmetric matrix are related as follows.

l_{ij}=u_{ji},\operatorname{where}i\neq j

(76)