An Analysis of Matrix Diagonalization: Analytical Tools to Maintain Numerical Accuracy

Use of matrices is common in multiple areas of academics. In various areas of science, multiple number of fields are found to interact with each other forming a coupled interacting system. The examples of those could be found in the areas of classical physics as well as sub nuclear physics where subnuclear particle like neutrino interact in flavor space and photon interact with (axion like particles ) ALP in a magnetized media during their propagation in space time. Studies of such systems require solving matrix equations to understand their space time evolution. The treatment here is suitable for neutrino oscillation. because the number of nonzero elements of the matrix mathb f M considered here are nine and could be complex. And M is considered to be normal that is having linearly independent eigen vectors.