Writing the general matrix transformation of coordinates as the matrix equation [ x ′ 0 x ′ 1 x ′ 2 x ′ 3 ] = [ Λ Λ 0 0 Λ Λ 0 1 Λ Λ 0 2 Λ Λ 0 3 Λ Λ 1 0 Λ Λ 1 1 Λ Λ 1 2 Λ Λ 1 3 Λ Λ 2 0 Λ Λ 2 1 Λ Λ 2 2 Λ Λ 2 3 Λ Λ 3 0 Λ Λ 3 1 Λ Λ 3 2 Λ Λ 3 3 ] [ x 0 x 1 x 2 x 3 ] allows the transformation of other physical quantities that cannot be expressed as four-vectors; e.g., tensors or spinors of any order in 4d spacetime, to be defined. In the corresponding tensor index notation, the above matrix expression is x ′ ν ν = Λ Λ ν ν μ μ x μ μ ,