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?

  • $\begingroup$ 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. $\endgroup$ – Patrick Da Silva Aug 12 '13 at 0:37
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    $\begingroup$ Was it George Wendt? $\endgroup$ – Cheerful Parsnip Aug 12 '13 at 0:38
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    $\begingroup$ Norman Vector Peale, in his book, "The Power of Positive Metrics." $\endgroup$ – Thomas Andrews Aug 12 '13 at 0:40
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    $\begingroup$ Maybe this and this are related (to the question). $\endgroup$ – Git Gud Aug 12 '13 at 0:40
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    $\begingroup$ Also possibly of interest: Etymology of the word “normal” (perpendicular). $\endgroup$ – MJD Aug 16 '13 at 16:28

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.

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