@amiloradovsky@functional.cafe Yeah, and for natural numbers there is a natural reason it is called multiplication. Multi means many, right? "Manyficiatoin" I guess. Same kind of word root appears in other languages I know. When they generalized they should have picked a different name. Like "ah, it's funny it kind of acts like multiplication, but it's definitely not, so lets come up with a name for it a poet won't be ashamed of, instead of abusing our language".

The straight forward way to define a multiplication on vectors is compponent-wise. It doesn't break anything, it is simply uninteresting, which is fitting for a basic operation. None of those other things should be called multiplication, IMHO.