%0 Journal Article %1 schneider %A Schneider, Hans %D 1986 %J Linear Algebra and its Applications %K eigenvalues graph.theory perron-frobenius principal.submatrix %N Supplement C %P 161--189 %R 10.1016/0024-3795(86)90313-7 %T The influence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: A survey %V 84 %X Abstract For a nonnegative matrix P, we discuss the relation of its marked reduced graph to that part of the Jordan form that is associated with the Perron-Frobenius root, to the nonnegativity of the eigenvectors and generalized eigenvectors, to the nonnegativity of solutions of linear equations, and to the asymptotic growth of powers of the matrix. Results are often stated in terms of M-matrices, and standard results on irreducible matrices are assumed. We give examples to illustrate the theorems surveyed.

@article{schneider, abstract = {Abstract For a nonnegative matrix P, we discuss the relation of its marked reduced graph to that part of the Jordan form that is associated with the Perron-Frobenius root, to the nonnegativity of the eigenvectors and generalized eigenvectors, to the nonnegativity of solutions of linear equations, and to the asymptotic growth of powers of the matrix. Results are often stated in terms of M-matrices, and standard results on irreducible matrices are assumed. We give examples to illustrate the theorems surveyed.}, added-at = {2017-11-20T03:20:35.000+0100}, author = {Schneider, Hans}, biburl = {https://www.bibsonomy.org/bibtex/2dffcb53f8c55a23b55d807f16b74a3d7/ytyoun}, doi = {10.1016/0024-3795(86)90313-7}, interhash = {9f3ac6606240c08d4e1ac51ed62fc69f}, intrahash = {dffcb53f8c55a23b55d807f16b74a3d7}, issn = {0024-3795}, journal = {Linear Algebra and its Applications}, keywords = {eigenvalues graph.theory perron-frobenius principal.submatrix}, number = {Supplement C}, pages = {161--189}, timestamp = {2017-11-20T03:20:35.000+0100}, title = {The influence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: A survey}, volume = 84, year = 1986 }