The Principle of Relativity

by Albert Einstein; H. Minkowski

(14) A^μν = A^νμ

or

(14a) A_μν = A_νμ.

It must be proved that a symmetry so defined is a property independent of the system of reference. It follows in fact from (9) remembering (14)

Antisymmetrical tensor.

A contravariant or co-variant tensor of the 2nd, 3rd or 4th rank is called antisymmetrical when the two components got by mutually interchanging any two indices are equal and opposite. The tensor or A^μν or A_μν is thus antisymmetrical when we have

(15) A^μν = -A^νμ

or

(15a) A_μν = -A_νμ.