A scalar expression for matrices with symplectic involution

Authors:
Louis Halle Rowen and Uri Schild

Journal:
Math. Comp. **32** (1978), 607-613

MSC:
Primary 16A28; Secondary 16A42

DOI:
https://doi.org/10.1090/S0025-5718-1978-0480620-5

MathSciNet review:
0480620

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Abstract: Various algebraic reductions are made to facilitate computer verification of the following result: If *x* and *y* are matrices such that [*x, y*] is regular, , and, with respect to the canonical symplectic involution, *x* is symmetric and *y* is antisymmetric, then the element satisfies a minimal equation of degree .

**[1]**A. A. ALBERT,*Structure of Algebras*, Amer. Math. Soc. Colloq. Publ., vol. 24, Amer. Math. Soc., Providence, R. I., 1961. MR**0123587 (23:A912)****[2]**N. JACOBSON,*Lectures in Abstract Algebra*II -*Linear Algebra*, Van Nostrand, Princeton, N. J., 1953. MR**0053905 (14:837e)****[3]**T. MUIR,*A Treatise on the Theory of Determinants*, Dover, New York, 1960. MR**0114826 (22:5644)****[4]**L. H. ROWEN, "Identities in algebras,"*Israel J. Math.*, v. 20, 1975, pp. 70-95. MR**0437585 (55:10509)****[5]**L. H. ROWEN, "Central simple algebras,"*Israel J. Math.*, 1978. MR**0491810 (58:11008)**

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0480620-5

Article copyright:
© Copyright 1978
American Mathematical Society