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The algebraic motivation for tensors is fairly good: we know how to deal with linear maps, we must deal with multilinear maps, so we want to reduce them to linear maps. The name tensor however seems to relate to something about tension and indeed tensors are widely used in Physics. Then, my first question is:

Where the name tensor comes from? Which was the first object conceived that way that today we consider a tensor?

And finally, how does this object that originated the name tensor relates to the rigorous definition. I mean, how did mathematicians realize that this object connected with some physical situation could be rigorously defined in terms of the universal property and so on?

Thanks very much in advance.

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I do know that tensors are used to represent the mechanical stress and strain at any given point in a solid material. I don't, however, know what a tensor is, so I can't give any details. –  dfeuer Nov 12 '13 at 21:37
    
I think when physicists use the term "tensor" they really mean "tensor field." I could be wrong though. –  Cameron Williams Nov 12 '13 at 21:41
    
According to Wikipedia the mathematicians came up with it first. Einstein then popularized its use in physics. –  zibadawa timmy Nov 12 '13 at 21:42

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