7.1 LDU Decomposition of Symmetric Matrices

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

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

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and

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

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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.

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

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