Tensor
A multilinear geometric object describing linear relationships between algebraic vectors, tensors, and scalars independent of coordinate choice.
Governing formula
T'^ij = (∂x'^i / ∂x^k) (∂x'^j / ∂x^l) T^kl
SI unit
Geometric Multilinear Object
In depth
Tensors generalize scalars (rank 0), vectors (rank 1), and matrices (rank 2) to higher dimensions. They maintain coordinate covariance under transformations, ensuring physical laws retain the same mathematical form in all coordinate systems.
Examples in the real world
The rank-2 Stress-Energy Tensor T_μν in General Relativity and the Moment of Inertia Tensor I_ij in rigid body mechanics.