Some analysis for block matrices with the Jordan canonical form

We describe implementations for the analysis of block matrices by a matrix equation, a nilpotent matrix, and the Jordan canonical form. For this work, some properties of block matrices such as sparsity, the companion form, matrix polynomials, etc. can help us in finding more results. These expressions can be used to describe a block matrix that simplifies many complex calculations independently in other research articles and activities for deeper work in this field.