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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 31st 2018

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

    v1, current

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2024

    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 ?

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2024

    I added a bit to the entry.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2024

    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).

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2024

    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

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeMay 30th 2024

    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