The adjoint matrix, sometimes also called the Adjugate Matrix, is defined by
![\begin{displaymath}
{\hbox{\sf A}}^\dagger \equiv ({\hbox{\sf A}}^{\rm T})^*,
\end{displaymath}](a_374.gif) |
(1) |
where the Adjoint Operator is denoted
and
denotes the Transpose. If a
Matrix is Self-Adjoint,
it is said to be Hermitian. The adjoint matrix of a Matrix product is given by
![\begin{displaymath}
{(ab)^\dagger}_{ij} \equiv [(ab)^{\rm T}]^*_{ij}\,.
\end{displaymath}](a_377.gif) |
(2) |
Using the property of transpose products that
it follows that
![\begin{displaymath}
({\hbox{\sf A}}{\hbox{\sf B}})^\dagger = {\hbox{\sf B}}^\dagger{\hbox{\sf A}}^\dagger.
\end{displaymath}](a_381.gif) |
(4) |
© 1996-9 Eric W. Weisstein
1999-05-25