Projection-based commuting solutions of the Yang-Baxter matrix equation for non-semisimple eigenvalues

Let A be a square matrix. We construct projection-based commuting solutions of the quadratic matrix equation AXA=XAX, which are associated with non-semisimple eigenvalues of A with at least one 1×1 Jordan block, based on special projections onto some subspaces of the corresponding generalized eigenspaces. The result extends the main one (Ding, Zhang, 2014) from the semisimple eigenvalue case to the non-semisimple one.