Dear All, I have a rank r positive-semidefinite matrix M, which I am trying to decompose via lower-triangularlar Cholesky factorization M=LL^\top, but I am particularly interested in computing an L that has r positive diagonal entries and n-r columns containing all zero. Such a Cholesky matrix exis…

For example, here is a rank-3 5x5 positive semidefinite matrix: julia> B = rand(3,5); A = Hermitian(B'B); cholesky(A) throws PosDefException, and cholesky(A, Val(true)) throws RankDeficientException. However, passing check=false forces the factorization to proceed even if it is rank-deficient: j…

You maybe want the “pivoted Cholesky” factorization , via cholesky(A, Val(true)), probably passing check=false. (Under the hood, this calls LAPACK’s dpstrf .) The central complication is that a positive-semidefinite matrix can easily become indefinite (slightly negative eigenvalues or pivots) due t…

Thanks so much, @stevengj for the very clear answer! Also, thanks for the dpstrf pointer, I will go through the LAPACK documentation.

Cholesky decomposition of low-rank positive-semidefinite matrix

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Cholesky decomposition of low-rank positive-semidefinite matrix

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