Abstract
LetA be a fixed 2×2 integral matrix with irrational characteristic roots. LetB be an arbitrary 2×2 integral matrix. It was previously shown that -det (AB-BA)=normλ, where λ is in the field of the characteristic roots ofA. It is now shown that the λ's corresponding to varyingB's can be chosen to form a fractional ideal in this field.
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Taussky, O.: Additive commutators between 2×2 integral matrix representations of orders in identical or different quadratic number fields. Bull. AMS74, 885–887 (1974).
Taussky, O.: Additive commutators of rational 2×2 matrices. J. Lin. Alg.12, 1–6 (1975).
Taussky, O.: Ideal matrices I. Arch. Math.13, 275–282 (1962).
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Dedicated to Prof. Dr. E. Hlawka on the occasion of his 60th birthday
This work was carried out (in part) under an NSF grant.
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Taussky, O. Norms in quadratic fields and their relations to non commuting 2×2 matrices I. Monatshefte für Mathematik 82, 253–255 (1976). https://doi.org/10.1007/BF01526330
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DOI: https://doi.org/10.1007/BF01526330