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Published March 1966 | public
Journal Article

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

Taussky, Olga


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.

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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