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I need to find the relation between [tex] E^{2}-B^{2} [/tex] and [tex] F_{\mu\nu} F^{\mu\nu} [/tex]

Actually, I need to use this relation to determine that the first is a scalar.

What I can't understand is how these notations match the formal definition:

If I multiply a matrix by another (same size) I should be receiving another matrix of the same size. Not a scalar...

But if I use the notations I need to use here:

[tex] F_{\mu\nu} F^{\mu\nu}\Rightarrow \Sigma_{i=1}^{3} \Sigma_{j=1}^{3} = F_{00}F^{00}+F_{01}F^{01}+...

[/tex] and that is not the product I expect it to be...

Could someone explain me how these definitions get along?

Thank you!