soher⬡⬢

A tensor generalizes vectors and matrices into higher-dimensional mathematical objects that describe relationships between multiple quantities. A vector is a 1D list, a matrix is a 2D grid, and a 3rd order tensor can be visualized as a 3D cube. The stress tensor σᵢⱼ represents internal forces within a material, while the Riemann curvature tensor R(u,v)w = ∇ᵤ∇ᵥw − ∇ᵥ∇ᵤw − ∇₍[u,v]₎w describes the curvature of spacetime in general relativity. Other concepts shown include the product derivative rule, the tensor product A ⊗ B, and the quantum state (1/√2)(|00⟩ + |11⟩). Tensors are indispensable in engineering, physics, machine learning, computer vision, and many other fields where multidimensional data and complex interactions must be modeled accurately.