Determination of the Most Stable Configuration Pair(s) of the Constituent Matrix Shells and the Set of Most Stable Configurations of the Corresponding Matrix Shell System

The present article addresses the issue of determining the most stable configuration pair(s) of a Matrix Shell, and thereby, of determining the set of most stable configurations of the associated Matrix Shell System. The problem is resolved using the criteria of spectral proximity w.r.t. the Ordered Eigenspectrum of a defined Baseline Matrix (both for Individual constituent Matrix Shells and the Matrix Shell System) and quantified in terms of an appropriate Proximity Function, the article presents the analytic expressions of the Matrix Shell Baseline elements, corresponding to A n A n A n A n (0,2 ), (0,2 1), (1,2 ), (1,2 1)   and A t n A t n ( ,2 ), ( ,2 1)  where t  2 , type Matrix Shells and defines the Baseline Matrices in terms of these Baseline elements, the article then provides a mathematical framework to determine the most stable Configuration pair(s) of constituent Matrix Shells and the set of most stable configurations of the Matrix Shell System and concludes with demonstration of the working of the presented framework through hypothetical examples based case studies