Sharp bounds on the spectral radius of a nonnegative matrix. (English) Zbl 1283.15058
Summary: We give upper and lower bounds for the spectral radius of a nonnegative matrix using its row sums and characterize the equality cases if the matrix is irreducible. Then we apply these bounds to various matrices associated with a graph, including the adjacency matrix, the signless Laplacian matrix, the distance matrix, the distance signless Laplacian matrix, and the reciprocal distance matrix. Some known results in the literature are generalized and improved.
MSC:
| 15A42 | Inequalities involving eigenvalues and eigenvectors |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
Keywords:
spectral radius; nonnegative matrix; graph; adjacency matrix; signless Laplacian matrix; distance matrixReferences:
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