Suppose we have a real matrix $A=R R^t$ where $R$ is triangular. Since there is no restriction on $R$ we can say that $A$ is positive semidefinite. Can I affirm that $A$ has LU decomposition (L lower triangular with ones on the diagonal and U upper triangular)?
2026-03-25 17:26:23.1774459583
Do positive semidefinite matrix have LU decomposition?
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