# 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 LDLT 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)