  We consider the eigenvalues and eigenvectors of an axisymmetric matrix$A$
with some special structures. We propose S-Oja-Brockett equation
$\frac{dX}{dt}=AXB-XBX^TSAX,$ where $X(t) \in {\mathbb R}^{n \times m}$ with $m
\leq n$, $S$ is a positive definite symmetric solution of the Sylvester
equation $A^TS = SA$ and $B$ is a real positive definite diagonal matrix whose
diagonal elements are distinct each other, and show the S-Oja-Brockett equation
has the global convergence to eigenvalues and its eigenvectors of $A$.
