Matrix inequalities by means of embedding.
Matrizen mit maximaler Diagonale bei unitärer Similarität.
Minimal Gerschgorin sets for partitioned matrices. II: The spectral conjecture.
Minimal Gerschgorin sets for partitioned matrices. III: Sharpness of boundaries and monotonicity as a function of the partition.
Negative powers and the spectrum of matrices
New bounds for the minimum eigenvalue of 𝓜-tensors
A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal. Appl., 2014, 2014, 114) and Zhao and Sang (J. Inequal. Appl., 2016, 2016, 268). Finally, two numerical examples are given to verify the theoretical results.
New bounds for the minimum eigenvalue of the Fan product of two -matrices
In this paper, we mainly use the properties of the minimum eigenvalue of the Fan product of -matrices and Cauchy-Schwarz inequality, and propose some new bounds for the minimum eigenvalue of the Fan product of two -matrices. These results involve the maximum absolute value of off-diagonal entries of each row. Hence, the lower bounds for the minimum eigenvalue are easily calculated in the practical examples. In theory, a comparison is given in this paper. Finally, to illustrate our results, a simple...
New bounds for the minimum eigenvalue ofM-matrices
Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.
Nonhermitian systems and pseudospectra
Four applications are outlined of pseudospectra of highly nonnormal linear operators.
Norms of certain rational functions of a matrix and Schur's criterion for polynomials
Norms of matrix powers
Obtaining bounds on the two norm of a matrix from the splitting lemma.
On a bound on algebraic connectivity: the case of equality
In a recent paper the authors proposed a lower bound on , where , , is an eigenvalue of a transition matrix of an ergodic Markov chain. The bound, which involved the group inverse of , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...
On a conjecture regarding characteristic polynomial of a matrix pair.
On a Theorem of Gersgorin.
On Bauer's Generalized Gershgorin Discs.
On condition numbers of a nondefective multiple eigenvalue.
On convexity, the Weyl group and the Iwasawa decomposition
On elementary symmetric functions of the eigenvalues of the sum and product of normal matrices
On Geršgorin-type problems and ovals of cassini.