When was the dot/scalar/inner (however you want to call it) product historically first abstractly introduced as a mapping that had to fulfill certain axioms ?
2026-04-06 23:22:24.1775517744
Historically first axiomatization of the inner product
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According to http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Abstract_linear_spaces.html, the scalar product was introduced by Grassmann in 1844, in a work that was rejected by other mathematicians for many years. Peano was apparently the first to give a clear and precise account of Grassmann's ideas in his 1888 book Geometrical Calculus (see http://www-history.mcs.st-andrews.ac.uk/Biographies/Peano.html)