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 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.