Tensor Visualization

Rank-0/1/2 tensors, coordinate transforms, metric tensor, Einstein summation

T^i_j transforms as: T'^i_j = Λ^i_k T^k_l (Λ⁻¹)^l_j  |  Tᵢⱼ = gᵢₖ T^k_j
A tensor is not just a matrix — it's a geometric object whose components transform precisely under coordinate changes. T^i_j transforms with one Λ and one Λ⁻¹. The metric tensor gᵢⱼ converts between upper (contravariant) and lower (covariant) indices: Vᵢ = gᵢⱼ V^j. Einstein summation: repeated upper/lower index means sum over all values.