Is it possible to generalize Magic Squares to infinite dimensional matrices?

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I know that magic squares exist: Summing over every row or column and diagonal one gets the same sum. My question is whether it is possible to generalize magic squares in such a way that the numbers are real and instead of summing over rows and diagonals one integrates over linear hypersurfaces and retrieves the same number. Has this been done already? How can I generate a family of distributions which satisfy this?