Some new properties of octonionic matrices

In this study, firstly, real, complex and quaternion combinations of octonionic matrices are defined. In terms of these defined combinations, basic operations of octonionic matrices are given. Later, algebraic structures of octonionic matrix set are obtained. In addition, the modulus structures of the octonionic matrix set on the real, complex and quaternion matrix sets are examined. Bases and dimension of octonionic matrix sets with modulus structure have been found. Finally, special octonionic matrices and transpose, conjugate, trace of octonionic matrices are given.