A scalar expression for matrices with symplectic involution
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- by Louis Halle Rowen and Uri Schild PDF
- Math. Comp. 32 (1978), 607-613 Request permission
Abstract:
Various algebraic reductions are made to facilitate computer verification of the following result: If x and y are $8 \times 8$ matrices such that [x, y] is regular, $\operatorname {tr} (x) = 0$ , and, with respect to the canonical symplectic involution, x is symmetric and y is antisymmetric, then the element ${(x + [x,y]x{[x,y]^{ - 1}})^2}$ satisfies a minimal equation of degree $\leqslant 2$.References
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- Nathan Jacobson, Lectures in abstract algebra. Vol. II. Linear algebra, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. MR 0053905
- Thomas Muir, A treatise on the theory of determinants, Dover Publications, Inc., New York, 1960. Revised and enlarged by William H. Metzler. MR 0114826
- Louis Halle Rowen, Identities in algebras with involution, Israel J. Math. 20 (1975), 70–95. MR 437585, DOI 10.1007/BF02756757
- Louis Halle Rowen, Central simple algebras, Israel J. Math. 29 (1978), no. 2-3, 285–301. MR 491810, DOI 10.1007/BF02762016
Additional Information
- © Copyright 1978 American Mathematical Society
- 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