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I blanked a section labeled "Algorithm", which presented a naive block of code doing .. something. There have got to dozens if not hundreds of algorithms that can be applied to triangular matrixes. This is not the right place for a compendium of these. Readers can be referred to github for LAPACK or BLAS. [[Special:Contributions/67.198.37.16|67.198.37.16]] ([[User talk:67.198.37.16|talk]]) 17:53, 4 February 2018 (UTC)
== Chapter: Forward and back substitution ==
The algorithm for forward substitution as it is now, assumes that <math>l_{i,i}\neq 0</math>, which isn't given in general.
Furthermore, the algorithm isn't well defined for triangular matrices that don't have a staircase form, e.g.
<math>\begin{pmatrix}0&1&1\\0&1&2\\0&0&0\end{pmatrix}</math>.
I'd therefore argue that this chapter, though generally formulated for triangular matrices, would be a better fit for [[Row_echelon_form]].
This would have the added benefit that the reduced row echelon form admits a generalized backward substitution algorithm, which handles the case of underdetermined systems, and returns all possible solutions (see discussion, row echelon form)
[[User:Sanitiy|Sanitiy]] ([[User talk:Sanitiy|talk]]) 17:42, 21 December 2019 (UTC)
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