I've just begun studying numerical approaches to LU decomposition and it got me thinking. Is there a more "general" (not sure if this is the right term for what I'm describing) form of LU decomposition? Meaning, do algorithms exist to solve A = L*X where L is a given nonsingular lower triangular matrix, and X is an unknown matrix. A would be the n-by-n matrix we are trying to factor here. I'm almost 100% sure it would be slower than LU. If someone could elaborate on this problem or point me to resources studying this that would be incredible, thank you!
2026-03-25 17:18:18.1774459098
generalization of LU decomposition?
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In fact, one such algorithm is simply Gaussian elimination... When you row reduce a non-singular matrix to an upper triangular form, the final result is the matrix $U$ ( or at least one possible matrix $U$) in the $LU$ decomposition. The $L$ matrix can also be recovered from the elementary transformation matrices used to perform row reduction.