  Let $m$, $n$, $a_1$, ..., $a_r$, $b_1$, ..., $b_r$ be integers with $1\leq
a_1<...<a_r\leq m$ and $1\leq b_1<...<b_r\leq n$. And let $x$ be the universal
$m\times n$ matrix with the property that $i$-minors of first $a_i-1$ rows and
first $b_i-1$ columns are all zero, for $i=1$, ..., $r+1$ ($a_{r+1}=m+1$ and
$b_{r+1}=n+1$). For an integer $u$ with $1\leq u\leq m$, we denote by $U$ the
$u\times n$ matrix consisting of the first $u$ rows of $x$. In this paper, we
consider the analytic spread and the reduction number of the ideal of maximal
minors of $U$
