Matrix bounds for the solution of the continuous algebraic Riccati equation.
Matrix equalities and inequalities involving Khatri-Rao and Tracy-Singh sums.
Matrix inequalities involving the Khatri-Rao product
We extend three inequalities involving the Hadamard product in three ways. First, the results are extended to any partitioned blocks Hermitian matrices. Second, the Hadamard product is replaced by the Khatri-Rao product. Third, the necessary and sufficient conditions under which equalities occur are presented. Thereby, we generalize two inequalities involving the Khatri–Rao product.
Matrix versions of the Cauchy and Kantorovich inequalities.
Maximizing the determinant for a special class of block-partitioned matrices.
Multiplicative principal-minor inequalities for a class of oscillatory matrices.
New trace bounds for the product of two matrices and their applications in the algebraic Riccati equation.
Norm estimates for functions of two commuting matrices.
Norm estimates for functions of two non-commuting matrices.
Norm estimates for the inverses of matrices of monotone type and totally positive matrices.
Note on the degree of concavity of the determinant on sets of positive definite quadratic forms.
Numerical ranges of an operator on an indefinite inner product space.
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 generalization of the Van Der Waerden conjecture
On a geometric property of positive definite matrices cone.
On a Schur complement inequality for the Hadamard product of certain totally nonnegative matrices.
On a variational problem for an infinite particle system in a random medium.
On an inequality involving power and contraction of matrices with and without trace.
On inequalities involving the Hadamard product of matrices.
On matrix convexity of the Moore-Penrose inverse.