The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each corresponding codimension is the number of conditions which a matrix of the given type must satisfy in order to have the specified multiplicities.

Significant progress has been made in convolutional neural networks (CNN) based gas recognition. However, existing electronic nose (e-Nose) algorithms all use the closed-set assumption that test and training samples are same label space can only detect objects of known classes. realistic scenarios, collecting data for every possible would waste much resource. Open-set identification aims to act...

Eigenvalues of a graph are the eigenvalues of its adjacency matrix. The multiset of eigenvalues is called its spectrum. There are many properties which can be explained using the spectrum like energy, connectedness, vertex connectivity, chromatic number, perfect matching etc. Laplacian spectrum is the multiset of eigenvalues of Laplacian matrix. The Laplacian energy of a graph is the sum of the...

It is well-known that exploiting label correlations is important to multi-label learning. Existing approaches either assume that the label correlations are global and shared by all instances; or that the label correlations are local and shared only by a data subset. In fact, in the real-world applications, both cases may occur that some label correlations are globally applicable and some are sh...

In this paper, a new approach is presented to determine common eigenvalues of two matrices. It is based on Gerschgorin theorem and Bisection method. The proposed approach is simple and can be useful in image processing and noise estimation. KeywordsCommon Eigenvalues, Gerschgorin theorem, Bisection method, real matrices. INTRODUCTION Eigenvalues play vary important role in engineering applicati...

We will discuss a few basic facts about the distribution of eigenvalues of the adjacency matrix, and some applications. Then we discuss the question of computing the eigenvalues of a symmetric matrix. 1 Eigenvalue distribution Let us consider a d-regular graph G on n vertices. Its adjacency matrix AG is an n× n symmetric matrix, with all of its eigenvalues lying in [−d, d]. How are the eigenval...

In the spiked population model introduced by Johnstone [10], the population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). The question is to quantify the effect of the perturbation caused by the spike eigenvalues. Baik and Silverstein [6] establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalue...

We study Schrödinger operators with Floquet boundary conditions on flat tori obtaining a spectral result giving an asymptotic expansion of all the eigenvalues. The is in λ−δ δ∈(0,1) for most eigenvalues λ (stable eigenvalues), while it “directional expansion” remaining (unstable eigenvalues). proof based structure theorem which variant one proved [31], [32] and new iterative quasimode argument.

We consider the eigenvalues of the matrix AKNS system and establish bounds on the location of eigenvalues and criteria for the nonexistence of eigenvalues. We also identify properties of the system which guarantee that eigenvalues cannot lie on the imaginary axis or can only lie on the imaginary axis. Moreover, we study the deficiency indices of the underlying non-selfadjoint differential opera...

Consider the linear general eigenvalue problem Ay = λBy , where A and B are both invertible and Hermitian N × N matrices. In this paper we construct a set of meromorphic functions, the Krein eigenvalues, whose zeros correspond to the real eigenvalues of the general eigenvalue problem. The Krein eigenvalues are generated by the Krein matrix, which is constructed through projections on the positi...