Quaternionic matrix: Difference between revisions

Revision as of 15:50, 2 September 2010

Revision as of 15:52, 2 September 2010

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u_{11}v_{11}+u_{12}v_{21} & u_{11}v_{12}+u_{12}v_{22}\\

u_{21}v_{11}+u_{22}v_{21} & u_{21}v_{12}+u_{22}v_{22}\\

\end{pmatrix}

</math>

=== 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 secondary diagonal there is an inversion of the first product.

:<math>

U =

\begin{pmatrix}

u_{11} & u_{12}\\

u_{21} & u_{22}\\

\end{pmatrix}

\quad

V =

\begin{pmatrix}

v_{11} & v_{12}\\

v_{21} & v_{22}\\

\end{pmatrix}

\quad

UV =

\begin{pmatrix}

u_{11}v_{11} + v_{21}u_{12} & v_{12}u_{11} + u_{12}v_{22}\\

v_{11}u_{21} + u_{22}v_{21} & u_{21}v_{12} + v_{22}u_{22}\\

\end{pmatrix}

</math>