Abstract. Let G be a simple undirected connected graph on n vertices. Suppose that the vertices of G are labelled 1,2, . . . ,n. Let di be the degree of the vertex i. The Randić matrix of G , denoted by R, is the n× n matrix whose (i, j)−entry is 1 √ did j if the vertices i and j are adjacent and 0 otherwise. The normalized Laplacian matrix of G is L = I−R, where I is the n× n identity matrix. ...

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. ...

When a square matrix A, is diagonalizable, (for example, when A is Hermitian or has distinct eigenvalues), then An can be written as a sum of the nth powers of its eigenvalues with matrix weights. However, if a 1 occurs in its Jordan form, then the form is more complicated: An can be written as a sum of polynomials of degree n in its eigenvalues with coefficients depending on n. In this case to...

We determine analytically the modulus of the second eigenvalue for the web hyperlink matrix used by Google for computing PageRank. Specifically, we prove the following statement: “For any matrix , where is an row-stochastic matrix, is a nonnegative rank-one row-stochastic matrix, and ! " , the second eigenvalue of has modulus # $&%'#( ) . Furthermore, if has at least two irreducible closed subs...

The set S(g, n) of all stochastic matrices of order n whose directed graph has girth g is considered. For any g and n, a lower bound is provided on the modulus of a subdominant eigenvalue of such a matrix in terms of g and n, and for the cases g = 1, 2, 3 the minimum possible modulus of a subdominant eigenvalue for a matrix in S(g, n) is computed. A class of examples for the case g = 4 is inves...

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. ...