Let A denote a square complex matrix and let E be a perturbation matrix. The purpose of this paper is to investigate the perturbation of the Drazin inverse when B = A + E satisfies the rank conditions rankA = rankB = rankAB, where r and s denote the indices of A and B, respectively. We will derive an explicit representation of B as a function of A and B −A , for certain positive integers j, k. ...

We extend the results in [5] to non-compactly supported perturbations for a class of symmetric first order systems. The purpose of this note is to extend the results obtained in [5] to non-compactly supported perturbations. Consider in R, n ≥ 3 odd, a first order matrix-valued differential operator of the form ∑n j=1A 0 jDxj , A 0 j being constant Hermitian d× d matrices, and denote by G0 its s...

We review the assumptions and the logic underlying the derivation of DLCQ Matrix models. In particular we try to clarify what remains valid at finite N , the role of the non-renormalization theorems and higher order terms in the supergravity expansion. The relation to Maldacena’s conjecture is also discussed. In particular the compactification of the Matrix model on T3 is compared to the AdS5 ×...

Neural network models are used to reveal the nonlinear winter atmospheric teleconnection patterns associated with the El Niño-Southern Oscillation (ENSO) and with the Arctic Oscillation (AO) over the N. Hemisphere. The nonlinear teleconnections (for surface air temperature, precipitation, sea level pressure and 500 hPa geopotential height) are found to relate quadratically to the ENSO and AO in...

We extend the technique of constructive expansions to compute the connected functions of matrix models in a uniform way as the size of the matrix increases. This provides the main missing ingredient for a non-perturbative construction of the φ 4 field theory on the Moyal four dimensional space.

We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In both cases we show that most of the eigenvalues of the perturbed matrix are very close to a circle with centre at the origin. In the case of random perturbations we obtain an estimate of the number of eigenvalues that are well inside the circle in a certain asymptotic regime. In the case of ...

Certain continuity properties of the factors in generalized polar decompositions of real and complex matrices are studied. A complete characterization is given of those generalized polar decompositions that persist under small perturbations in the matrix and in the scalar product. Connections are made with quadratic matrix equations, and with stability properties of certain invariant subspaces.

Let A denote a square complex matrix and let E be a perturbation matrix. The purpose of this paper is to investigate the perturbation of the Drazin inverse when B = A + E satisfies the rank conditions rankA = rankB = rankAB, where r and s denote the indices of A and B, respectively. We will derive an explicit representation of B as a function of A and B −A , for certain positive integers j, k. ...