A note on the largest eigenvalue of non-regular graphs.
A note on the matrix Haffian.
This note contains a transparent presentation of the matrix Haffian. A basic theorem links this matrix and the differential ofthe matrix function under investigation, viz ∇F(X) and dF(X).Frequent use is being made of matrix derivatives as developed by Magnus and Neudecker.
A Note on the Permanental Roots of Bipartite Graphs
It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing...
A note on the ranks of set-inclusion matrices.
A note on the reverse order laws for - and -inverses of multiple matrix products.
A note on the scalar Haffian.
In this note a uniform transparent presentation of the scalar Haffian will be given. Some well-known results will be generalized. A link will be established between the scalar Haffian and the derivative matrix as developed by Magnus and Neudecker.
A note on the spectra of tridiagonal matrices.
A Note on the Structure of the Semigroup of Doubly-Stochastic Matrices
A note on the trace inequality for products of Hermitian matrix power.
A Note on two Indices of Semigroup Elements
A note on ultrametric matrices
It is proved in this paper that special generalized ultrametric and special matrices are, in a sense, extremal matrices in the boundary of the set of generalized ultrametric and matrices, respectively. Moreover, we present a new class of inverse -matrices which generalizes the class of matrices.
A novel interpretation of least squares solution.
A Numerical Procedure for Computing the Moore-Penrose Inverse.
A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix
It is shown that if A is a bounded linear operator on a complex Hilbert space, then , where w(A) and ||A|| are the numerical radius and the usual operator norm of A, respectively. An application of this inequality is given to obtain a new estimate for the numerical radius of the Frobenius companion matrix. Bounds for the zeros of polynomials are also given.
A p-adic Perron-Frobenius theorem
We prove that if an n×n matrix defined over ℚ ₚ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ℚ ₚ, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a p-adic analogue of the Perron-Frobenius theorem for positive real matrices.
A parallel algorithm for computing the group inverse via Perron complementation.
A parameterized lower bound for the smallest singular value.
A pencil approach to high gain feedback and generalized state space systems
A pointwise approximation of isolated trees in a random graph.
A polynomial time spectra decomposition test for certain classes of inverse M-matrices.