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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
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 $ 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$.

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Article copyright: © Copyright 1978 American Mathematical Society