Talk:Gram–Schmidt process

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Does anyone know when the Gram Schimdt process was discovered? And who Mr. Gram and Mr. Schmidt are?

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Jørgen Pedersen Gram (1850-1916), Danish mathematician.

Sebastjan

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I was going to rewrite the process in terms of projections to clean it up a bit, but I'll probably stuff it up somewhere and be shouted at. So, if you feel up to doing so, I think it'd clear up the process greatly. Dysprosia 01:41, 26 Aug 2004 (UTC)

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I changed the calculation of u_2 etc. to use projection onto u_1 instead of onto e_1. This allows the process to work in fields where you cannot take square roots, such as the rationals. I have a program that produces a series of orthogonal vectors spanning the right space. norm@cap-lore.com .

Ewwwwww, I really don't like the notation proj_u v. If anything it should be written proj_v u, to emphasize that the projection is just a scaling of u.

[edit] Maybe we need an illustration

Maybe we need an illustration of the projection just like most text books.

I just created this…

…would it fulfill its purpose? –Gustavb 07:16, 18 February 2006 (UTC)

Yes, I guess that is basically it. However, I think that u₂ is too long. We need to have

so the direction of u₂ is correct, but it should only go up to the dashed line. Does that make sense to you? If not, I'll change the picture myself, but I don't know the TeX package you are using (it looks quite easy to use though). -- Jitse Niesen (talk) 14:52, 18 February 2006 (UTC)

Yes, of course…guess I was tired when I did it. I have now created a new one but unfortunately I can't upload it due to a restriction in wikimedia commons which only allows users registered for more than four days to replace files (I registered yesterday.) –Gustavb 15:24, 18 February 2006 (UTC)

That seems rather silly to me; what's the purpose of prohibiting somebody from overwriting their own files? If you want, you can email it to me at my-first-name@ma.hw.ac.uk (making the obvious substitution) and I'll upload it on your behalf. You can also just wait a couple of days. -- Jitse Niesen (talk) 15:49, 18 February 2006 (UTC)

I don't think it checks who uploaded the original file – it just block all uploads for the purpose of reducing vandalism (I assume). So yes, it's a bad solution. Thanks for uploading the new version. –Gustavb 16:27, 18 February 2006 (UTC)