Inverse spread limit of a nonnegative matrix
نویسندگان
چکیده
For a given nonnegative n × n matrix A consider the following quantity s(A) := mini,j(A)ij maxi,j(A)ij , m = 1, 2, . . . as long as the denominator is positive. It is simply the ratio between the smallest and the largest entries of Am. We call s(Am) the inverse spread of Am which is interpreted as a measure of the maximum variation among the entries of Am in the multiplicative and reciprocal sense. Smaller s(Am) means a larger variation for Am. Clearly 0 ≤ s(Am) ≤ 1 for all m = 1, 2, . . . We study the asymptotic behavior of s(Am), that is, the behavior of s(Am) as m →∞. The study arises from evolutionary biology.
منابع مشابه
On the nonnegative inverse eigenvalue problem of traditional matrices
In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
متن کاملA Modified Digital Image Watermarking Scheme Based on Nonnegative Matrix Factorization
This paper presents a modified digital image watermarking method based on nonnegative matrix factorization. Firstly, host image is factorized to the product of three nonnegative matrices. Then, the centric matrix is transferred to discrete cosine transform domain. Watermark is embedded in low frequency band of this matrix and next, the reverse of the transform is computed. Finally, watermarked ...
متن کاملA Modified Digital Image Watermarking Scheme Based on Nonnegative Matrix Factorization
This paper presents a modified digital image watermarking method based on nonnegative matrix factorization. Firstly, host image is factorized to the product of three nonnegative matrices. Then, the centric matrix is transferred to discrete cosine transform domain. Watermark is embedded in low frequency band of this matrix and next, the reverse of the transform is computed. Finally, watermarked ...
متن کاملNEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS
We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System $(FFLS)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. First, in discussing an $FFLS$ with a nonnegative coefficient matrix, we consider an equivalent $FFLS$ by using an appropriate permutation to simplify fuzzy multiplications. T...
متن کاملOn the construction of symmetric nonnegative matrix with prescribed Ritz values
In this paper for a given prescribed Ritz values that satisfy in the some special conditions, we find a symmetric nonnegative matrix, such that the given set be its Ritz values.
متن کامل