As is well known, the Schur complements of strictly or irreducibly diagonally dominant matrices are H−matrices; however, the same is not true of generally diagonally dominant matrices. This paper proposes some conditions on the generally diagonally dominant matrix A and the subset α ⊂ {1, 2, . . . , n} so that the Schur complement matrix A/α is an H−matrix. These conditions are then applied to ...

This paper gives double angle theorems that bound the change in an invariant subspace of an indeenite Hermitian matrix in the graded form H = D AD subject to a perturbation H ! e H = D (A + A)D. These theorems extend recent results on a deenite Hermitian matrix in the graded form (Linear Algebra Appl., 311 (2000), 45{60) but the bounds here are more complicated in that they depend on not only r...

Mitochondria must maintain volume homeostasis in order to carry out oxidative phosphorylation. It has been postulated that the concentration of free Mg2+([Mg2+]) serves as the sensor of matrix volume and regulates a K+-extruding K+/H+antiport (K. D. Garlid. J. Biol. Chem. 255: 11273-11279, 1980). To test this hypothesis, the fluorescent probe furaptra was used to monitor [Mg2+] and free Ca2+ co...

Let P (h), h ∈]0,1] be a semiclassical scalar differential operator of order 2. The existence of a supersymmetric structure given by a matrix G(x;h) was exhibited in [9] under rather general assumptions. In this note we give a sufficient condition the coefficients of P (h) so that the matrix G(x;h) enjoys some nice estimates with respect to the semiclassical parameter.

In this paper, we consider the H∞ controller design problem for both continuous-time and discrete-time linear time-invariant (LTI) systems via low order dynamic output feedback controllers. The existence condition of desired H∞ controllers is expressed as a feasibility problem of a bilinear matrix inequality (BMI) with respect to a coefficient matrix defining the controller and a Lyapunov matri...

A complete and minimum set of necessary and sufficient conditions for a real 4x4 matrix to be a physical Mueller matrix is obtained. An additional condition is presented to complete the set of known conditions, namely the four conditions obtained from the non-negativity of the eigenvalues of the Hermitian matrix H associated with a Mueller matrix M and the Transmittance Condition. Using the pro...

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n×d matrix W and a nonnegative d×m matrix H. NMF has a wide variety of applications, including bioinformatics, chemometrics, communication complexity, machine learning, polyhedral combinatorics, among many others. A longstanding open question, posed by Cohen an...

Let B be an m × n (m ≥ n) complex (or real) matrix. It is known that there is a unique polar decomposition B = QH, where Q∗Q = I, the n× n identity matrix, and H is positive definite, provided that B has full column rank. If B is perturbed to B̃, how do the polar factors Q and H change? This question has been investigated quite extensively, but most work so far has been on how the perturbation c...

Newton-Raphson State Estimation method using bus admittance matrix remains as an efficient and most popular method to estimate the state variables. Elements of Jacobian matrix are computed from standard expressions which lack physical significance. In this paper, elements of the state estimation Jacobian matrix are obtained considering the power flow measurements in the network elements. These ...