tensor, in mathematics, quantity that depends linearly on several vector variables and that varies covariantly with respect to some variables and contravariantly with respect to others when the coordinate axes are rotated (see Cartesian coordinates). Tensors appear throughout mathematics, though they were first treated systematically in the calculus of differential forms and in differential geometry. They play an important role in mathematical physics, particularly in the theory of relativity. Tensors are also important in the theory of elasticity, where they are used to describe stress and strain. The study of tensors was formerly known as the absolute differential calculus but is now called simply tensor analysis.
See R. Abraham et al., Manifolds, Tensor Analysis, and Applications (1988).