Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...

In this paper we study eigenvalue problems for hemivariational inequalities driven by the p-Laplacian differential operator. We prove the existence of positive smooth solutions for both non-resonant and resonant problems at the principal eigenvalue of the negative p-Laplacian with homogeneous Dirichlet boundary condition. We also examine problems which are near resonance both from the left and ...

We present a new numerical iterative method for computing selected eigenpairs of a right definite two-parameter eigenvalue problem. The method works even without good initial approximations and is able to tackle large problems that are too expensive for existing methods. The new method is similar to the Jacobi–Davidson method for the eigenvalue problem. In each step, we first compute Ritz pairs...

The superscript H refers to the Hermitian transpose, which includes transposition and complex conjugation. That is, for any matrix A, AH = AT . An eigenvector of A, as defined above, is sometimes called a right eigenvector of A, to distinguish from a left eigenvector. It can be seen that if y is a left eigenvector of A with eigenvalue λ, then y is also a right eigenvector of AH , with eigenvalu...

The superscript H refers to the Hermitian transpose, which includes transposition and complex conjugation. That is, for any matrix A, AH = AT . An eigenvector of A, as defined above, is sometimes called a right eigenvector of A, to distinguish from a left eigenvector. It can be seen that if y is a left eigenvector of A with eigenvalue , then y is also a right eigenvector of AH , with eigenvalue...

In this paper, we propose a new method to obtain the eigenvalues and fuzzy triangular eigenvectors of matrix $$\left( {\tilde{A}} \right)$$ , where elements are given. For purpose, solve 1-cut eigenvectors. Considering interval system $$\left[ \right]_{\alpha } \left[ {\tilde{X}} = {\tilde{\lambda }} 0 \le \alpha 1$$ as α-cut $$\tilde{A}\tilde{X} \tilde{\lambda }\tilde{X}$$ determine left right...

Some new estimates for the eigenvalue decay rate of the Lyapunov equation AX + XA = B with a low rank right-hand side B are derived. The new bounds show that the right-hand side B can greatly influence the eigenvalue decay rate of the solution. This suggests a new choice of the ADI-parameters for the iterative solution. The advantage of these new parameters is illustrated on second order damped...

We adopt the concept of the correlation matrix to study correlations among sequences of time-extended events occurring repeatedly at consecutive time intervals. As an application we analyze the magnetoencephalography recordings obtained from the human auditory cortex in the epoch mode during the delivery of sound stimuli to the left or right ear. We look into statistical properties and the eige...