Statistical Convergence of Matrix Sequences and Eigenvalue Influences

This paper delves into the statistical convergence of sequences of square matrices with entries in the real or complex domain. Matrix sequence convergence is traditionally examined through two distinct lenses: element-wise convergence and norm convergence. We explore both paradigms, unraveling their interconnections through illustrative examples. Furthermore, we shed light on the intrinsic nature of matrix sequence convergence, emphasizing its intricate dependence on the eigenvalues of the matrices involved.