The recursively-constructed family of Mandelbrot matrices $M_n$ for $n=1$, $2$, $\ldots$ have nonnegative entries (indeed just $0$ and $1$, so each can be called a binary matrix) eigenvalues whose negatives $-\lambda = c$ give periodic orbits under the iteration, namely $z_k z_{k-1}^2+c$ with $z_0=0$, are thus contained in set. By Perron--Frobenius theorem, dominant real positive eigenvalue, wh...

To solve large-scale matrix eigenvalue problems (EVPs), a two-step tridiagonalization method using the block Householder transformation (HT) is often employed. Although based on dense arithmetic requires memory storage of O(N2) and an operations O(N3), in this study, these were reduced by approximating low-rank (BLR-) matrices. A special HT for BLR-matrices it are proposed to EVP with real symm...

Similar to the well known Schur Horn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a Hermitian matrix the Sing Thompson theorem characterizes the relationship between the diagonal en tries and the singular values of an arbitrary matrix It is noted in this paper that based on the induction principle such a matrix can be constructed numerically by...

Ritz method is one of the techniques for reduction of the degrees of freedom. Efficiency of Ritz method depends on used vectors. The Ritz method uses load depended vectors in spite of modal method and for this reason it is expected to give better results than modal method. This is the advantage of Ritz method. It is worth mention that the mode shapes are independent of loading. The vectors that...

In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian on graphs discuss its rigidity. As applications the eigenvalues, Lichnerowicz-type estimates some combinatorial for graphs.

In this paper, we consider the application of the homotopy perturbation method (HPM) to compute the eigenvalues of the Sturm-Liouville problem (SLP) which is called non-definite SLP. Two important Examples show that HPM is reliable method for computing the eigenvalues of SLP.

Abstract Violation of the no-signaling principle may occur in PT-symmetric evolutions, that is, evolutions stem from Hamiltonians are symmetric with respect to parity and time-reversal, bipartite entangled states. The violation can be avoided by using a non-conventional inner product. We show even within formalism utilizes conventional product between physical state vectors separable Hilbert sp...

Eigenvalues and eigenvectors of covariance matrices are important statistics for multivariate problems in many applications, including quantitative genetics. Estimates of these quantities are subject to different types of bias. This article reviews and extends the existing theory on these biases, considering a balanced one-way classification and restricted maximum-likelihood estimation. Biases ...