Sometimes only square matrices can be diagonalized

Levy, Lawrence S.

doi:10.1090/S0002-9939-1975-0376775-2

Sometimes only square matrices can be diagonalized
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by Lawrence S. Levy

Proc. Amer. Math. Soc. 52 (1975), 18-22

DOI: https://doi.org/10.1090/S0002-9939-1975-0376775-2

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Abstract:

It is proved that every SQUARE matrix over a serial ring is equivalent to some diagonal matrix, even though there are rectangular matrices over these rings which cannot be diagonalized.

References

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Serial rings, semihereditary rings, and finitely presented modules