PAUL HALMOS Celebrating 50 Years of Mathematics pp 237-255 | Cite as

# On Products of Involutions

## 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## Preview

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