The Principle of Relativity

by Albert Einstein; H. Minkowski

"(A)"

According to (31) and (29), the last member can take the form

"(B)"

Both the first members of the expression (B), and the second member of the expression (A) cancel each other, since the naming of the summation-indices is immaterial. The last member of (B) can then be united with first of (A). If we put

g^μν A_μ = A^ν,

where A^ν as well as A_μ are vectors which can be arbitrarily chosen, we obtain finally

This scalar is the Divergence of the contravariant four-vector A^ν.

Rotation of the (covariant) four-vector.