On Products of Involutions

William H. Gustafson
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William H. Gustafson: Texas Technical University, Department of Mathematics

A chapter in PAUL HALMOS Celebrating 50 Years of Mathematics, 1991, pp 237-255 from Springer

Abstract: Abstract In 1974, A. Sampson [16] gave a rather technical matrix-theoretic proof that any complex matrix of determinant ±1 can be written as a product of finitely many involutions. A brash, young (at the time) algebraist, I quickly saw a group-theoretic proof that gives the same result for matrices over any field, and involves very little computation. Indeed, my proof occupied one and a half typed pages, most of it devoted to a couple of special cases. I sent a copy off to Hans Schneider for publication in Linear Algebra and its Applications, and distributed copies in the mailboxes of a few selected colleagues. One of those colleagues was Paul Halmos (that was a different time and place for both of us). A few hours later, Paul passed me in the hall.

Keywords: Normal Subgroup; Simple Group; Companion Matrix; Finite Order; Companion Matrice (search for similar items in EconPapers)
Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0967-6_27

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DOI: 10.1007/978-1-4612-0967-6_27

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