Quaternionic matrix: Difference between revisions

Revision as of 21:10, 3 July 2010

Revision as of 21:19, 3 July 2010

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A '''quaternionic matrix''' is a [[matrix]] whose elements are [[quaternion]]s.

== Product of two quaternionic matrices ==

The product of two quaternionic matrices is either ''hamiltonian'' or ''octonionic'', depending on whether the order of multiplication of the entries is preserved. The quaternion field, <math>\mathbb{H}</math>, is a non-commutative field, so the product of two quaternionic matrices may or may not preserve the order of multiplication.

=== Hamiltonian product ===

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=== Octonionic product ===

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

:<math>

U =

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*[[Octonion]]

[[Category:Calculation by MatrixMatrices]]

[[Category:Linear algebra]]