New lower bounds on eigenvalue of the Hadamard product of an \(M\)-matrix and its inverse

DOI10.1016/j.laa.2008.11.002zbMath1163.15019OpenAlexW1973342845MaRDI QIDQ999820

Fu-Bin Chen, Yao-Tang Li, De-Feng Wang

Publication date: 10 February 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.11.002

zbMATH Keywords

Hadamard product\(M\)-matrixnonnegative matrixlower boundsminimum eigenvaluedoubly stochastic

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48) Stochastic matrices (15B51)

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Cites Work

• Unnamed Item
• Lower bounds for the minimum eigenvalue of Hadamard product of an \(M\)-matrix and its inverse
• A trace inequality for M-matrices and the symmetrizability of a real matrix by a positive diagonal matrix
• An inequality for the Hadamard product of an M-matrix and an inverse M- matrix
• On a conjecture of Fiedler and Markham
• Proof of a conjecture of Fiedler and Markham
• A lower bound for the minimum eigenvalue of the Hadamard product of matrices
• On an inequality for the Hadamard product of an \(M\)-matrix and its inverse
• Some inequalities for the Hadamard product and the Fan product of matrices
• Minimal Gerschgorin sets
• A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices