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(mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array.

The second-order Cauchy stress tensor ${\displaystyle \mathbf {T} }$ describes the stress experienced by a material at a given point. For any unit vector ${\displaystyle \mathbf {v} }$, the product ${\displaystyle \mathbf {T} \cdot \mathbf {v} }$ is a vector, denoted ${\displaystyle \mathbf {T} (\mathbf {v} )}$, that quantifies the force per area along the plane perpendicular to ${\displaystyle \mathbf {v} }$. This image shows, for cube faces perpendicular to ${\displaystyle \mathbf {e} _{1},\mathbf {e} _{2},\mathbf {e} _{3}}$, the corresponding stress vectors ${\displaystyle \mathbf {T} (\mathbf {e} _{1}),\mathbf {T} (\mathbf {e} _{2}),\mathbf {T} (\mathbf {e} _{3})}$ along those faces. Because the stress tensor takes one vector as input and gives one vector as output, it is a second-order tensor.

(engineering, computing) A multidimensional array with (at least) two dimensions.

Neural network with tensors as node values

(mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array.

Comparison of the first five orders of tensors