Matrix Inequalities for Iterative Systems
Auteur : Taubig Hanjo
The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.
Introduction. Notation and Basic Facts. Motivation.Diagonalization and Spectral Decomposition. Undirected Graphs / Hermitian Matrices. General Results. Restricted Graph Classes. Directed Graphs / Nonsymmetric. Walks and Alternating Walks in Directed Graphs. Powers of Row and Column Sums. Applications. Bounds for the Largest Eigenvalue. Iterated Kernels.Conclusion. Bibliography. Index.
Date de parution : 03-2021
17.8x25.4 cm
Date de parution : 11-2016
17.8x25.4 cm
Thèmes de Matrix Inequalities for Iterative Systems :
Mots-clés :
Undirected Graph; Directed Graphs; Nonnegative Matrices; Nonnegative Symmetric Matrix; Adjacency Matrix; Hermitian Matrices; Zagreb Indices; Entry Sum; Hermitian Matrix; Bipartite Graphs; Nonnegative Vector; De Bruijn Graphs; Dx Dy; Positive Semidefinite Matrices; Rayleigh Ritz Theorem; Extremal Graph Theory; Nonnegative Matrix; Index Λ1; Largest Eigenvalue Λ1; Degree Sequence; Vertex Vj; Perron Frobenius Theorem; Eigenvalues Λi; Vertex Degrees; Hamiltonian Cycle