just for calculation purposes. That way, each row of the first matrix (1234), and each column of the second matrix (5678), point to the cell of the result that they produce. Of course, these matrices can be larger than 2x2; often 3x3 or 4x4 are used, but any size is allowed.

In simple index notation, this is written where i, j and k all range over 1, 2. Notice how the index j, in between, disappears; this is the essence of tensor contraction.

In Einstein notation, this would be

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