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On Products of Involutions

In: PAUL HALMOS Celebrating 50 Years of Mathematics

Author

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  • William H. Gustafson

    (Texas Technical University, Department of Mathematics)

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.

Suggested Citation

  • William H. Gustafson, 1991. "On Products of Involutions," Springer Books, in: John H. Ewing & F. W. Gehring (ed.), PAUL HALMOS Celebrating 50 Years of Mathematics, pages 237-255, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0967-6_27
    DOI: 10.1007/978-1-4612-0967-6_27
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