# LDLt factorization for full matrices

**URL:** <https://discourse.julialang.org/t/ldlt-factorization-for-full-matrices/75356>\
**Category:** Numerics\
**Tags:** question, linearalgebra\
**Created:** [January 28, 2022, 12:09pm UTC](https://discourse.julialang.org/t/ldlt-factorization-for-full-matrices/75356 "2022-01-28T12:09:26Z")\
**Posts on this page:** 1\
**Showing post:** 21

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**Author:** ![mancolric](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mancolric/32/21799_2.png) [@mancolric](https://discourse.julialang.org/u/mancolric)\
**Post date:** [May 23, 2022, 3:12pm UTC](https://discourse.julialang.org/t/ldlt-factorization-for-full-matrices/75356/21 "2022-05-23T15:12:57Z")

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Yes, I meant by D to a 1 \times 1 block diagonal matrix.

The example you have given to show that a PLDL^TP^T factorization may not exist is very helpful.

From the REPL help, it seems to me that `ldlt` does no pivoting on `SymTridiagonal` matrices, but it does on `SparseMatrixCSC`. However, this factorization is still not useful because, as you say, it may not exist — and indeed yields an error in your example. By the way, [here](https://discourse.julialang.org/t/ldlt-factorization-for-sparse-matrix/57011) is some help to retrieve the factors from the `ldlt` decomposition.

So, now it is more clear to me that `bunchkaufman` is the best option. However, it works only for full matrices. In the case of sparse matrices, is there any `bunchkaufman` factorization? In Matlab there seems to be a stable LBL^T (B=block diagonal) [factorization](https://www.mathworks.com/help/matlab/ref/ldl.html#bqwmk97-1) both for dense and sparse matrices. I have not found anything similar in Julia.

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