Tensor
Definition
A generalization of scalars, vectors, and matrices — stress, inertia, and spacetime curvature are all tensors.
Technical definition
A multilinear map: rank-0 is a scalar, rank-1 a vector, rank-2 matrix-like. Components transform by fixed rules under coordinate changes.
Example
The stress tensor's 9 components describe every force on a tiny cube of material — pressure, shear, everything.
Common confusion
'Tensor' doesn't just mean 'fancy matrix' — the defining feature is how components transform between coordinate systems. A random 3×3 table of numbers isn't a tensor.