# Dictionary:Tensor

A set of functions of the coordinates. A rectangular array of coefficients for a system of linear equations. Concerned with how point functions change with a change in coordinates, that is, how a function transforms into another coordinate system. If a tensor can be expressed in terms of partial derivatives of one coordinate set with respect to another, it is an **Einstein-Ricci tensor**; for example,

where *P*_{n}^{i}(*x*) and *P*_{n}^{i}(*y*) represent stresses in the *x*- and *y*-coordinate systems, respectively. Tensors of identical type are **parallel**. The **norm** of a tensor equals the sum of the squares of its components, that is, the square of its **magnitude**. The **scalar product** of two tensors equals the sum of the products of corresponding components; it also equals the product of the two magnitudes multiplied by the cosine of the **generalized angle** between the tensors. Nonzero stress and strain tensors are **mutually orthogonal** if the corresponding strain-energy density vanishes.