The Principle of Relativity

by Albert Einstein; H. Minkowski

from which it is easy to see that the tensor is antisymmetrical.

Divergence of the Six-vector.

If (27) is multiplied by g^μα g^νβ (mixed multiplication), then a tensor is obtained. The first member of the right hand side of (27) can be written in the form

If we replace g^μα g^νβ A_μνσ by A_σ^αβ, g^μα g^νβ A_μν by A^αβ and replace in the transformed first member

∂g^νβ/∂x_σ and ∂g^μα/∂x_σ

with the help of (34), then from the right-hand side of (27) there arises an expression with seven terms, of which four cancel. There remains

"(38)"

This is the expression for the extension of a contravariant tensor of the second rank; extensions can also be formed for corresponding contravariant tensors of higher and lower ranks.