A tensor is a generalization of scalars, vectors, and matrices to an arbitrary number of indices.

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges over the number of dimensions of space. However, the dimension of the space is largely irrelevant in most tensor equations (with the notable exception of the contracted Kronecker delta). Tensors are generalizations of scalars (that have no indices), vectors (that have exactly one index), and matrices (that have exactly two indices) to an arbitrary number of indices.

antisymmetric tensor | array | Cartesian tensor | comma derivative | contravariant tensor | covariant derivative | covariant tensor | curl | divergence | gradient | index gymnastics | index lowering | index raising | irreducible tensor | isotropic tensor | Jacobi tensor | matrix | mixed tensor | Ricci curvature tensor | Riemann tensor | scalar | symmetric tensor | tensor contraction | tensor space | torsion tensor | vector | Weyl tensor

graduate school level