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arXiv · 2504.14198

Linear maps preserving product of involutions

Chi-Kwong Li·Tejbir Lohan·Sushil Singla
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Abstract

An element of the algebra $M_n(\mathbb{F})$ of $n \times n$ matrices over a field $\mathbb{F}$ is called an involution if its square equals the identity matrix. Gustafson, Halmos, and Radjavi proved that any product of involutions in $M_n(\mathbb{F})$ can be expressed as a product of at most four involutions. In this article, we investigate the bijective linear preservers of the sets of products of two, three, or four involutions in $M_n(\mathbb{F})$.

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Chi-Kwong Li, Tejbir Lohan, Sushil Singla. 2026-03-18. Linear maps preserving product of involutions. https://arxiv.org/abs/2504.14198

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