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Tensor

Mathematically, a tensor is a single point or collection of points in space (or space-time) that transform according to certain rules under a change of coordinates. In physics, tensors are used to characterize certain properties of a physical system (spin, charge, etc.), also useful for transformation operations.

If the elements represent a continuum of points, the tensor is a function of position and may form a tensor field. Tensors are common in differential equations of mathematical physics, so the methods of differential calculus can be applied to tensors. A single number tensor is referred to as a zero order tensor, or a scalar. A scalar is a zero-dimensional array that varies from point to point, becoming a scalar field.

A tensor of order one is a vector. It may be defined as a single point or array of points that vary continuously. In the latter case the order one tensor becomes a vector field. A second order tensor is an inertia matrix. The number of components in a tensor order is the number of dimensions in which the transformations are to take place.

Web Resources On Tensor

Tensor (Wikipedia)
Tensor (Wolfram MathWorld)

Book Resources On Tensor

Introduction to Tensor Calculus and Continuum Mechanics by J.H. Heinbockel
Vector and Tensor Analysis with Applications by A.I. Borisenko

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