Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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
   • PermaLink
   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