A bound for the spectral variation of two matrices.
A contribution to Collatz's eigenvalue inclusion theorem for nonnegative irreducible matrices.
A counterexample to Merikoski-Kumar conjecture on the product of normal matrices.
A geometric proof of the Perron-Frobenius theorem.
We obtain an elementary geometrical proof of the classical Perron-Frobenius theorem for non-negative matrices A by using the Brouwer fixed-point theorem and by studying the dynamics of the action of A on convenient subsets of Rn.
A lower bound sequence for the minimum eigenvalue of Hadamard product of an -matrix and its inverse
We propose a lower bound sequence for the minimum eigenvalue of Hadamard product of an -matrix and its inverse, in terms of an -type eigenvalues inclusion set and inequality scaling techniques. In addition, it is proved that the lower bound sequence converges. Several numerical experiments are given to demonstrate that the lower bound sequence is sharper than some existing ones in most cases.
A Method of Solving the Stability Problem for Complex Matrices.
A Minimaximin Formula and its Application to Doubly Stochastic Matrices
A new Geršgorin-type eigenvalue inclusion set.
A new upper bound for the eigenvalues of the continuous algebraic Riccati equation.
A note on estimate of the spectral radius of symmetric matrices
A note on estimates for the spectral radius of a nonnegative matrix.
A note on generalized Perron complements of -matrices.
A note on nonnegative matrices
A note on the trace inequality for products of Hermitian matrix power.
A parameterized lower bound for the smallest singular value.
A quantitative extension of the Perron-Frobenius theorem for doubly stochastic matrices
A Relative Backward Perturbation Theorem for the Eigenvalue Problem.
A review of selected topics in majorization theory
In this expository paper, some recent developments in majorization theory are reviewed. Selected topics on group majorizations, group-induced cone orderings, Eaton triples, normal decomposition systems and similarly separable vectors are discussed. Special attention is devoted to majorization inequalities. A unified approach is presented for proving majorization relations for eigenvalues and singular values of matrices. Some methods based on the Chebyshev functional and similarly separable vectors...
A survey of certain trace inequalities
This paper concerns inequalities like TrA ≤ TrB, where A and B are certain Hermitian complex matrices and Tr stands for the trace. In most cases A and B will be exponential or logarithmic expressions of some other matrices. Due to the interest of the author in quantum statistical mechanics, the possible applications of the trace inequalities will be commented from time to time. Several inequalities treated below have been established in the context of Hilbert space operators or operator algebras....
A Trace Inequality of John von Neumann.