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On the similarity transformation between an integral matrix with irreducible characteristic polynomial and its transpose

Taussky, Olga (1966) On the similarity transformation between an integral matrix with irreducible characteristic polynomial and its transpose. Mathematische Annalen, 166 (1). pp. 60-63. ISSN 0025-5831. doi:10.1007/bf01361438. https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904669

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Abstract

Let A and S be matrices of rational integers and let A have a characteristic polynomial f which is irreducible over the rationals. Let (1) S⁻¹AS = A'. A great deal can be said about the structure of all possible S's. In first place S is symmetric by an earlier result of H. ZASSENHAUS and O. TAUSSKY [3]. In 2. an explicit expression for S will be given which is already contained in FADDEEV [2], TAUSSKY [4], BENDER [1]. In 3. the determinant of S is discussed. In 4. a fractional ideal associated with the set of all solutions of (1) is constructed.


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https://doi.org/10.1007/bf01361438DOIArticle
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Additional Information:© 1966 Springer. (Received January 24, 1966) To O. H. KELLER on his sixtieth birthday. This work was carried out (in part) under National Science Foundation Grant GP 3909. The author gratefully acknowledges several helpful remarks by E. C. DADE.
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Funding AgencyGrant Number
NSFGP 3909
Issue or Number:1
DOI:10.1007/bf01361438
Record Number:CaltechAUTHORS:20201022-100904669
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201022-100904669
Official Citation:Taussky, O. On the similarity transformation between an integral matrix with irreducible characteristic polynomial and its transpose. Math. Ann. 166, 60–63 (1966). https://doi.org/10.1007/BF01361438
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106210
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:22 Oct 2020 22:33
Last Modified:16 Nov 2021 18:51

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