  In this paper, we introduce innovative approaches for accelerating the Jacobi
method for matrix diagonalization, specifically through the formulation of
large matrix diagonalization as a Semi-Markov Decision Process and small matrix
diagonalization as a Markov Decision Process. Furthermore, we examine the
potential of utilizing scalable architecture between different-sized matrices.
During a short training period, our method discovered a significant reduction
in the number of steps required for diagonalization and exhibited efficient
inference capabilities. Importantly, this approach demonstrated possible
scalability to large-sized matrices, indicating its potential for wide-ranging
applicability. Upon training completion, we obtain action-state probabilities
and transition graphs, which depict transitions between different states. These
outputs not only provide insights into the diagonalization process but also
pave the way for cost savings pertinent to large-scale matrices. The
advancements made in this research enhance the efficacy and scalability of
matrix diagonalization, pushing for new possibilities for deployment in
practical applications in scientific and engineering domains.
