Taussky, Olga (1976) Norms in quadratic fields and their relations to non commuting 2×2 matrices I. Monatshefte für Mathematik, 82 (3). pp. 253-255. ISSN 0026-9255. doi:10.1007/bf01526330. https://resolver.caltech.edu/CaltechAUTHORS:20201013-104023229
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Abstract
Let A be a fixed 2×2 integral matrix with irrational characteristic roots. Let B be an arbitrary 2×2 integral matrix. It was previously shown that -det (AB-BA) = norm λ, where λ is in the field of the characteristic roots of A. It is now shown that the λ's corresponding to varying B's can be chosen to form a fractional ideal in this field.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1976 Springer. (Received 31 October 1975) 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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| Subject Keywords: | Explicit Construction; Characteristic Root; Integral Ideal; Quadratic Field; Ideal Matrice | |||||||||
| Issue or Number: | 3 | |||||||||
| DOI: | 10.1007/bf01526330 | |||||||||
| Record Number: | CaltechAUTHORS:20201013-104023229 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20201013-104023229 | |||||||||
| Official Citation: | 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 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 106019 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 13 Oct 2020 18:18 | |||||||||
| Last Modified: | 16 Nov 2021 18:49 |
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