Due to the growing size of the matrices used in applications, it is useful to carefully distinguish between
some groups of matrix algorithms. We propose to use algebraic classi cation as the main way to group matrix algorithms. From an algorithmic point of view, we propose to highlight the class of block-recursive algorithms. These algorithms make it possible to ensure a uniform load of a computing cluster, to solve the problem of protecting against failure of its individual nodes, and, in addition, they have the complexity of matrix multiplication.