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In mathematics, we say that a an $n$th-rank tensor in $m$-dimensional space essentially takes $n$ vectors of dimension $n$ each and converts them into a scalar. Then what do we mean when we say that physical quantities like stress are tensors?

Qmechanic
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sixtyTonneAngel
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  • The word stress is vague, there are mechanical stress tensor , stress energy tensor, electromagnetic stress tensor, for example. I guess you mean a physical example of mechanical stress ?https://en.wikipedia.org/wiki/Viscous_stress_tensor –  Sep 18 '16 at 17:43
  • Comment to the post (v2): The word scalar is in mathematical or in physical sense? – Qmechanic Sep 18 '16 at 17:48
  • Related: http://physics.stackexchange.com/q/32011/2451 , http://physics.stackexchange.com/q/155857/2451 and links therein. – Qmechanic Sep 18 '16 at 17:52
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    There's no difference between the "mathematical" and "physical" meanings of tensors. For example, the stress tensor in physics takes in a vector (unit normal to a plane) and outputs a vector (force on that plane), so it's a (1, 1) tensor. – knzhou Sep 18 '16 at 17:52
  • Be aware that a tensor in mathematical terms is a tensor product of one forms and vectors, so your definition is not quite correct. – Sanya Sep 18 '16 at 17:59

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