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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 31st 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexa stub, for the moment just so as to make links work <a href="https://ncatlab.org/nlab/revision/Gaussian+elimination/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Gaussian+elimination">current</a>

   a stub, for the moment just so as to make links work

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeMay 19th 2024
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   Author: zskoda
   Format: MarkdownItexI do not understand the section "In constructive mathematics". The algorithms consists of steps involving algebraic operations which make sense in any unital ring as long as corresponding expressions are invertible. I mean, maybe we need to formulate the condition of the steps as invertibility of certain expressions in the field, instead of being non-zero, but what else can get wrong ?

   I do not understand the section “In constructive mathematics”. The algorithms consists of steps involving algebraic operations which make sense in any unital ring as long as corresponding expressions are invertible. I mean, maybe we need to formulate the condition of the steps as invertibility of certain expressions in the field, instead of being non-zero, but what else can get wrong ?

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeMay 19th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI added a bit to the entry.

   I added a bit to the entry.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeMay 19th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIn fact, if the system has a different number of equations and unknowns we should not talk about upper triangular matrices but rather row echelon forms, [wikipedia](https://en.wikipedia.org/wiki/Row_echelon_form). At least this is the usual terminology, I do not see how to rewrite without much adding (what I can not do now).

   In fact, if the system has a different number of equations and unknowns we should not talk about upper triangular matrices but rather row echelon forms, wikipedia. At least this is the usual terminology, I do not see how to rewrite without much adding (what I can not do now).

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 19th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe paragraph claiming that Gaussian elimination does not work over the real numbers was added by "Anonymous" in [revision 3](https://ncatlab.org/nlab/revision/diff/Gaussian+elimination/3). I am deleting it hereby. If anyone knows what was meant here, let's add it back in with proper explanation. <a href="https://ncatlab.org/nlab/revision/diff/Gaussian+elimination/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/Gaussian+elimination/5">v5</a>, <a href="https://ncatlab.org/nlab/show/Gaussian+elimination">current</a>

   The paragraph claiming that Gaussian elimination does not work over the real numbers was added by “Anonymous” in revision 3.

   I am deleting it hereby. If anyone knows what was meant here, let’s add it back in with proper explanation.

   diff, v5, current

6. • CommentRowNumber6.
   • CommentAuthorzskoda
   • CommentTimeMay 30th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItexAn application of Gauss elimination to a particular system yields the [[Gram-Schmidt orthogonalization]]: * Lyle Pursell, S. Y. Trimble, _Gram-Schmidt orthogonalization by Gauss elimination_, The American Mathematical Monthly __98__:6 (1991) 544--549 [doi](https://doi.org/10.1080/00029890.1991.11995755)

   An application of Gauss elimination to a particular system yields the Gram-Schmidt orthogonalization:

   • Lyle Pursell, S. Y. Trimble, Gram-Schmidt orthogonalization by Gauss elimination, The American Mathematical Monthly 98:6 (1991) 544–549 doi