This paper gives max characterizations for the sum of the largest eigen-values of a symmetric matrix. The elements which achieve the maximum provide a concise characterization of the generalized gradient of the eigenvalue sum in terms of a dual matrix. The dual matrix provides the information required to either verify rst-order optimality conditions at a point or to generate a descent direction...

We show a lower bound on mixing time for a non-reversible Markov chain in terms of its eigenvalues. This is used to show a bound on the real part of the complex-valued eigenvalues in terms of the realvalued eigenvalues of a related reversible chain, and likewise to bound the second largest magnitude eigenvalue. A myriad of Cheeger-like inequalities also follow for non-reversible chains, which e...

A Toeplitz de-noising method using the maximum eigenvalue is proposed for the voice activity detection at low SNR scenarios. This method uses the self-correlation sequence of speech bandwidth spectrum to construct a new symmetric Toeplitz matrix and to compute the largest eigenvalue, and the double decision thresholds in the largest eigenvalue are applied in the decision framewok. Simulation re...

Given a rectangle A and a set S of n points in A, the maximum empty rectangle problem is that of finding a largest-area rectangle which is contained in A. has its sides parallel to Ihose ofA. and does Dot contain any of the points in S. This Dote describes an efficient algorithm for solving this problem.

2 Eigenvalues of graphs 5 2.1 Matrices associated with graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The largest eigenvalue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Adjacency matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.3...

in this paper, we present an edge detection method based on wavelet transform and hessian matrix of image at each pixel. many methods which based on wavelet transform, use wavelet transform to approximate the gradient of image and detect edges by searching the modulus maximum of gradient vectors. in our scheme, we use wavelet transform to approximate hessian matrix of image at each pixel, too. ...

In this note we prove that {0, 1, √ 2, √ 3, 2} is the set of all real numbers ` such that the following holds: every tree having an eigenvalue which is larger than ` has a subtree whose largest eigenvalue is `.

We analyze the largest eigenvalue and eigenvector for the adjacency matrices of sparse random graph. Let λ1 be the largest eigenvalue of an n-vertex graph, and v1 be its corresponding normalized eigenvector. For graphs of average degree d log n, where d is a large enough constant, we show λ1 = d log n + 1 ± o(1) and 〈1, v1〉 = √ n ( 1−Θ ( 1 logn )) . It shows a limitation of the existing method ...

In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.

The purpose of this paper is to show that the joint numerical range of am-tuple of n×n hermitian matrices is convex whenever the largest eigenvalue of an associated family of hermitian matrices parameterized by the (m − 1)-dimensional sphere has constant multiplicity and, as a more technical condition, the union over the sphere of the largest eigenvalue eigenspaces does not fill the full n-dime...