# References for traceless and/or imaginary Octonionic matrices?

Hi all.

I was wondering if anyone has seen any work related to either traceless matrices of Octonions (with trace defined as the sum of diagonal) or matrices of pure imaginary Octonions (meaning real part of the matrix is a matrix of zeros).

That being said, my only experience with octonionic matrices is the 27-dimensional exceptional Jordan algebra, described for example here. It consists of $3\times 3$ hermitian octonionic matrices and the Jordan product is given by the symmetrised product.