We study (homogeneous and inhomogeneous) anisotropic Besov spaces associated to expansive dilation matrices $A\in \mathrm{GL}(d,\mathbb{R})$, with the goal of clarifying when two such matrices induce the same scale of Besov spaces. For this purpose, we first establish that anisotropic Besov spaces have an alternative description as decomposition spaces. This result allows to relate properties of function spaces to combinatorial properties of the underlying coverings. This principle is applied to the question of classifying dilation matrices. It turns out that the scales of homogeneous and inhomogeneous Besov spaces differ in the way they depend on the dilation matrix: Two matrices $A,B$ that induce the same scale of homogeneous Besov spaces also induce the same scale of inhomogeneous spaces, but the converse of this statement is generally false. We give a complete characterization of the different types of equivalence in terms of the Jordan normal forms of $A,B$.

我们研究与膨胀扩张矩阵有关的（均匀和不均匀）各向异性Besov空间 $\mathrm{一种}\in \mathrm{GL}（d，\mathbb{[R}）$，目的是弄清两个这样的矩阵何时诱发相同规模的Besov空间。为此，我们首先确定各向异性Besov空间具有替代描述作为分解空间。该结果允许将功能空间的属性与基础覆盖物的组合属性相关联。该原理适用于对膨胀矩阵进行分类的问题。结果表明，齐次和不齐次Besov空间的尺度在它们依赖于膨胀矩阵的方式上有所不同：两个矩阵$\mathrm{一种}，乙$诱导相同规模的齐次Besov空间的那些也诱导相同规模的不均匀空间，但是这种说法的反面通常是错误的。我们以约旦范式形式完整地描述了不同类型的等价形式$\mathrm{一种}，乙$。