  A holographic algorithm solves a problem in domain of size $n$, by reducing
it to counting perfect matchings in planar graphs. It may simulate a $n$-value
variable by a bunch of $t$ matchgate bits, which has $2^t$ values. The
transformation in the simulation can be expressed as a $n \times 2^t$ matrix
$M$, called the base of the holographic algorithm. We wonder whether more
matchgate bits bring us more powerful holographic algorithms. In another word,
whether we can solve the same original problem, with a collapsed base of size
$n \times 2^{r}$, where $r<t$.
  Base collapse was discovered for small domain $n=2,3,4$. For $n=3, 4$, the
base collapse was proved under the condition that there is a full rank
generator. We prove for any $n$, the base collapse to a $r\leq \lfloor \log n
\rfloor$, with some similar conditions. One of them is that the original
problem is defined by one symmetric function. In the proof, we utilize
elementary matchgate transformations instead of matchgate identities.
