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Quaternionic matrix

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Definition

One talk about quaternionic matrix when the elements are quaternions.

Product of two quaternionic matrix

The product of two quaternionic matrix is or hamiltonian or octonionic. The field is a non-commutative field , so the product of two quaternionic matrix has or not to preserve the order of the multiplication .

Hamiltonian product

The hamiltonian product preserves the order of the multiplication.

Octonionic product

The octonionic product does not preserve the order of the multiplication : on the main diagonal , there is an inversion of the second product and on the second diagonal there is an inversion of the first products.

See also