Lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and its inverse
Copyright policy )Lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and its inverse
This detailed paper proves algebraically a conjecture by \textit{M. Fiedler} and \textit{T. L. Markham} [Linear Algebra Appl, 101, 1--8 (1988; Zbl 0648.15009)] for the Hadamard product of a matrix and its inverse by refining Fiedler's and Markham's lower bounds for the minimum eigenvalue of that product. The main results are well demonstrated by an example at the end of the paper, in which the author's show their bounds and their improvement over Fiedler's and Markham's.
- Liaocheng University China (People's Republic of)
- University of Electronic Science and Technology of China China (People's Republic of)
Perron-Frobenius theorem, Numerical Analysis, Hadamard product, \(M\)-matrix, Algebra and Number Theory, eigenvalue, Fiedler and Markham's conjecture, Eigenvalue, inverse \(M\)-matrix, Inequalities involving eigenvalues and eigenvectors, Fiedler and Markham’s conjecture, Discrete Mathematics and Combinatorics, Theory of matrix inversion and generalized inverses, Geometry and Topology, M-matrix, Inverse, doubly stochastic matrices
Perron-Frobenius theorem, Numerical Analysis, Hadamard product, \(M\)-matrix, Algebra and Number Theory, eigenvalue, Fiedler and Markham's conjecture, Eigenvalue, inverse \(M\)-matrix, Inequalities involving eigenvalues and eigenvectors, Fiedler and Markham’s conjecture, Discrete Mathematics and Combinatorics, Theory of matrix inversion and generalized inverses, Geometry and Topology, M-matrix, Inverse, doubly stochastic matrices
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