"Matrix mappings preserving Diedonne determinant and their
algorithmic constructions"
Elena Kreines
Department of Mechanics and Mathematics, Moscow State University.
ABSTRACT.
In this paper the following problem is considered: let $D$
be a skew-field, $M_n(D)$ be a matrix algebra over its center
$K$. A classification of one-to-one $K$-linear mappings from
$M_n(D)$ to $M_n(D)$ which preserves Diedonne determinant is
obtained. Namely, $T(A)=P(A^s)Q$ for all matrices $A$ from
$M_n(D)$ or $T(A)=P( (A^s)^t )Q$ for all matrices $A$ from
$M_n(D)$, here $s$ denotes $K$-linear authomorphism of the
skew-field $D$, and $t$ denotes transpose matrix.
Computational algorithms for constracting matrices $P$ and
$Q$ are proposed.