张量（tensor）是一个可用来表示在一些矢量、纯量和其他张量之间的线性关系的多线性函数，这些线性关系的基本例子有内积、外积、线性映射以及笛卡儿积。其坐标在   维空间内，有  个分量的一种量，其中每个分量都是坐标的函数，而在坐标变换时，这些分量也依照某些规则作线性变换。称为该张量的秩或阶（与矩阵的秩和阶均无关系）。

在同构的意义下，第零阶张量（）为纯量，第一阶张量（）为矢量， 第二阶张量（）则成为矩阵。例如，对于3维空间，时的张量为此矢量：。由于变换方式的不同，张量分成协变张量（指标在下者）、逆变张量（指标在上者）、混合张量（指标在上和指标在下两者都有）三类。

Tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors. Elementary examples of such relations include the dot product, the cross product, and linear maps. Euclidean vectors, often used in physics and engineering applications, and scalars themselves are also tensors. A more sophisticated example is the Cauchy stress tensor T, which takes a direction v as input and produces the stress T on the surface normal to this vector for output, thus expressing a relationship between these two vectors, shown in the figure (right).