Abstract

In this paper, we show the convergence of matrix series and the conditions for their convergence by finding an upper bound for some specific matrix inequalities. Finally, we introduce a new form of arithmetic-geometric matrix series and analyze their convergence.

Keywords: Harmonic series; condition number of a matrix; Hilbert-Schmidt norm; norm inequality; positive definite matrix; singular value; spectral norm; matrix convergence.

DOI: 10.57016/MV-YNCe1669

Pages:  108--117     

Volume  78 ,  Issue  2 ,  2026