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My son, studying something equivalent to highschool, has to do a work about some topic in mathematics. The topic has to be some important and "fruitful" theorem (why is important, who stated it, who used it, what are the far reaching consequences...) I think is not far from the idea to choose this operation, the dot product, as it maintains the point about the fruitful thing (I have not to explain the central rôle it has in elemental analitic geometry and in general all derived from its more abstact definition in algebraic structures)

But my question is about the origin or history of this useful tool, e.g. who put it into the vector spaces, what and when we can consider as the first use of it. Of course, any ideas not related to the history part will be welcome too.

Added

It'd be interesting too to know who extended this concept to other areas and when.

Thanks in advance.

Rafa Budría
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  • Thank you very much. My fault. But I don't delete the question: In the question linked and its answers I have some very useful information, but it can be understood that I am asking here too about the generalizations and later incorporation to, e.g. algebraic structures... – Rafa Budría Jul 07 '17 at 16:53
  • I recommend he work through Chapter 3 of Elementary Differential. Geometry. Revised Second Edition. (it's not hard to find this text). Basically, it studies the structure of isometries of euclidean space. – James S. Cook Jul 07 '17 at 17:14
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    I'm not fully convinced this is an exact duplicate of that other question. The other question, since that is only about the history of the dot product. It doesn't ask for a summary of the role of the dot product in mathematics that explains its importance. – Michael Hardy Jul 07 '17 at 17:47

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