If a matrix $A$ is reducible, it is always possible to find a permutation matrix $P$ such that $PAP^{\intercal}$ has the block triangular form $$ PAP^{\intercal}=\begin{pmatrix}A_{11} & A_{12} & \cdots & A_{1n}\\ & A_{22} & \cdots & A_{2n}\\ & & \ddots & \vdots\\ & & & A_{nn} \end{pmatrix} $$ where each matrix $A_{ii}$ on the diagonal is either irreducible or a $1\times1$ zero matrix.
In the book Matrix Iterative Analysis, Richard S. Varga refers to this as a normal form of a matrix. However, the name normal form is not particularly telling, as there are various forms referred to as normal (i.e., Jordan normal form, Smith normal form, etc.). Is there a better name for $PAP^{\intercal}$ that is standard in the literature?