Changes

The rules for really correct tensor notation, including Einstein Summation, are as follows:

The rules for really correct tensor notation, including Einstein Summation, are as follows:

:Einstein summation must be over one subscript and one superscript.

:Einstein summation must be over one subscript and one superscript.

:Indices that appear in terms to be added or subtracted, or on opposite sides of and equals sign, must match: subscript for subscript, and superscript for superscript.

:Indices that appear in terms to be added or subtracted, or on opposite sides of and equals sign, must match: subscript for subscript, and superscript for superscript.

:For any index left over after summation, there is an implicit "for all" in the equation.

:For any index left over after summation, there is an implicit "for all" in the equation.

So the above equation becomes just

So the above equation becomes just