Timeline for Uniqueness and invariance of the LDLT decomposition
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 14, 2016 at 22:29 | comment | added | Federico Poloni | @user3749105 No -- just take a random positive definite matrix, and different choices for $P$ will give different factors $D$. I don't really think there is any meaningful uniqueness result, apart from the one I have stated in my answer ($LDL^\top$ without permutation, positive definite $A$). | |
| Feb 14, 2016 at 22:17 | comment | added | user3749105 | @Poloni: $D$ seems unique, or not? | |
| Feb 14, 2016 at 22:04 | comment | added | Federico Poloni | @user3749105 There are non-zero counterexamples as well. For instance, take $\begin{bmatrix}0 &0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$. | |
| Feb 14, 2016 at 21:54 | comment | added | user3749105 | Thanks. Actually, what is important to me is uniqueness up to a permutation. This is the purpose of question (b). $A = 0$ is kind of pathological example. Is $LDL^T$, or $L$ or $D$ unique for positive semi-definite matrices (except for $A = 0$)? I mean, $P$ is obviously not unique because of (b), so the question is what about the other matrices? | |
| Feb 13, 2016 at 12:16 | history | answered | Federico Poloni | CC BY-SA 3.0 |