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On pairs of matrices (of order two) A,B satisfying the conditione AeB=eA+B≠eBeA

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References

  1. W. Givens, Review of [2],Mathematical Review, Vol. 14, No. 3 (1953) p. 237.

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  2. M. Fréchet, “Les solutions non commutables de l'équation matriciellee XeY=eX+Y”,Rendiconti del Circolo Matematico di Palermo, s. 2, t. 1 (1952), pp. 11–27.

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  3. J. v. Neumann, “Über die analytischen Eingenschaften von Gruppen linearer Transformationen und ihrer Darstellungen”,Mathematische Zeitschrift Bd. 30, (1929), pp. 3–42.

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  4. W. J. Thron,The Theory of Functions of a Complex Variable, John Wiley and Sons, Inc., New York (1953), p. 216.

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  5. M. Fréchet, “Rectification”,Rendiconti del Circolo Matematico di Palermo fasc. 1, t. 2 (1953), p. 71.

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The author is indebted to Professor Gerald B. Huff for independently giving an exemple of a pair of matricesX, Y, such thate XeY=eX+Y≠eYeX and for suggesting this investigation.

Research sponsored by the Office of Ordinance Research, U. S. Army, under Contract DA-01-009-ORD-194.

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Huff, C.W. On pairs of matrices (of order two) A,B satisfying the conditione AeB=eA+B≠eBeA . Rend. Circ. Mat. Palermo 2, 326–330 (1953). https://doi.org/10.1007/BF02843709

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