B. Chauhan

Bounds on the Minimum Eigenvalue Modulus for Hadamard Products of $\mathbf{M}$- and $\mathbf{H}$-Matrices and Their Inverses

The quantity $q(A\circ A^{-1})$, the minimum modulus of the eigenvalues of $A\circ A^{-1}$, arises naturally in connection with positive diagonal symmetrizability. For an invertible $\mathbf{M}$-matrix $A$ of order $n$, the classical bounds $\frac{2}{n}\leq q(A\circ A^{-1})\leq 1$ are known. We discuss the sharpness of...