I've always been curious about the motivation behind the use of the word norm, as used in linear algebra and functional analysis, for a function that assigns a positive number to a vector.
Who introduced this term into mathematics?
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I guess the world itself looks a bit weird if you forget all the times we've used it in math, it's not really suggestive. – Patrick Da Silva Aug 12 '13 at 00:37
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3Was it George Wendt? – Cheerful Parsnip Aug 12 '13 at 00:38
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I think it comes from normal as questions about objects being normal to a plane or a line occurred in mathematics far before abstract norms were created. Though this is pure conjecture. – PVAL-inactive Aug 12 '13 at 00:39
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2Norman Vector Peale, in his book, "The Power of Positive Metrics." – Thomas Andrews Aug 12 '13 at 00:40
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1Maybe this and this are related (to the question). – Git Gud Aug 12 '13 at 00:40
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I wonder if it's related to the term "normal" (as in perpendicular). – rurouniwallace Aug 12 '13 at 00:53
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Could be related to the fact that the length of a vector has components that are normal to each other and the length is computed using these "normal" components – Anthony Peter Aug 12 '13 at 01:31
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2Also possibly of interest: Etymology of the word “normal” (perpendicular). – MJD Aug 16 '13 at 16:28
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I don't have personal insight into this question, but I do have Google! According to Steven Schwartzman's The Words of Mathematics, "norm" derives from the Latin norma meaning "carpenter's square", which explains its meaning of perpendicularity and measuring a unit. According to Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics, "norm" was first used in number theory by Gauss in 1832, for the Gaussian integers. From there, it was imported into analysis by Albert A. Bennett in 1921 and by Banach in 1922.
Chris Culter
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