If A has an LDU-factorization, then A is positive definite.

Name: If A has an LDU-factorization, then A is positive definite.
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Quizplus · Accepted Answer

An LDU-factorization, where a matrix A is factored into a lower triangular matrix L, a diagonal matrix D, and an upper triangular matrix U, does not necessarily imply that A is positive definite. Positive definiteness is a separate property that requires all eigenvalues of A to be positive, which is not guaranteed by having an LDU-factorization.

If a Has an LDU-Factorization, Then a Is Positive Definite