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arXiv · 2512.22134

A Mnemonic Matrix Rule for (Split) Octonionic Multiplication and its Extension to the Cayley--Dickson Tower

Jean-Pierre Gazeau
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Abstract

We present a compact mnemonic device for computing the product of two (split) octonions written in Cayley--Dickson form q+l p with q,p in H. The rule appears as a simple (R+L) pattern of right-ordered and left-ordered (quaternionic) products inside a 2X2 quaternionic matrix model. The pattern extends verbatim to all algebras in the Cayley--Dickson tower, providing an efficient computational tool in non-associative settings. To our knowledge, this explicit ``(R+L)'' mnemonic does not appear in the classical literature on octonions or composition algebras.

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Jean-Pierre Gazeau. 2025-12-10. A Mnemonic Matrix Rule for (Split) Octonionic Multiplication and its Extension to the Cayley--Dickson Tower. https://arxiv.org/abs/2512.22134

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