  Let $\mu_{M,D}$ be the self-affine measure generated by an expanding integer
matrix $M\in M_n(\mathbb{Z})$ and a finite digit set $D\subset\mathbb{Z}^n$. It
is well known that the two measures $\mu_{M,D}$ and $\mu_{\tilde{M},\tilde{D}}$
have the same spectrality if $\tilde{M}=B^{-1}MB$ and $\tilde{D}=B^{-1}D$,
where $B\in M_n(\mathbb{R})$ is a nonsingular matrix. This fact is usually used
to simplify the digit set $D$ or the expanding matrix $M$. However, it often
transforms integer digit set $D$ or expanding matrix $M$ into real, which
brings many difficulties to study the spectrality of
$\mu_{\tilde{M},\tilde{D}}$. In this paper, we introduce a similarity
transformation of general linear group $GL_n(p)$ for some self-affine measures,
and discuss their spectrality. This kind of similarity transformation can keep
the integer properties of $D$ and $M$ simultaneously, which leads to many
advantages in discussing the spectrality of self-affine measures. As an
application, we extend some well-known spectral self-affine measures to more
general forms.
