New Lower Bounds for the Minimum Eigenvalues of Hadamard Product in M-matrices

For lower bounds on the minimum eigenvalue of the Hadamard product of M-matrix A and the inverse of M-matrix B, it has been concerned with research by many scholars in recent years. This paper first introduces the background, then discusses the lower bounds for the minimum eigenvalue of the Hadamard product * of two nonsingular M-matrices *B by using Cauchy-Schwitz inequality*, Jacobi iterative matrix and the relationship between matrix eigenvalue and eigenvector and obtains the following new lower bounds: *Finally, the given numerical example shows that the estimating formula of the bound improves several existing results in some cases.(* Indicates a formula, please see the full text)