Tensor

A tensor is a mathematical object. Tensors provide a mathematical framework for solving physics problems in areas such as elasticity, fluid mechanics and general relativity.^[1] The word tensor comes from the Latin word tendere meaning "to stretch".

A tensor of order zero (zeroth-order tensor) is a scalar (simple number).^[2] A tensor of order one (first-order tensor) is a linear map that maps every vector into a scalar.^[2] A vector is a tensor of order one.^[2] A tensor of order two (second-order tensor) is a linear map that maps every vector into a vector (e.g. a matrix).^[2]

In linear algebra, the tensor product of two vector spaces ${\displaystyle V_{1}}$ and ${\displaystyle V_{2}}$, ${\displaystyle V_{1}\otimes V_{2}}$,^[3] is itself a vector space. It is a way of creating a new vector space analogous of multiplication of integers.^[4]

1. ↑ Rowland, Todd; Weisstein, Eric W. "Tensor". Wolfram Research. Retrieved 2016-02-19.
2. ↑ ^{2.0 2.1 2.2 2.3} Danielson, D. A. (1997). Vectors and Tensors in Engineering and Physics (Second ed.). Reading, Massachusetts: Addison-Wesley. p. 17. ISBN 0-201-44210-8.
3. ↑ "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-09-07.
4. ↑ Weisstein, Eric W. "Vector Space Tensor Product". mathworld.wolfram.com. Retrieved 2020-09-07.