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Minimal c p rank.

Shaked-Monderer, Naomi (2001)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix

Hiroshi Kurata, Ravindra B. Bapat (2016)

Special Matrices

By a hollow symmetric matrix we mean a symmetric matrix with zero diagonal elements. The notion contains those of predistance matrix and Euclidean distance matrix as its special cases. By a centered symmetric matrix we mean a symmetric matrix with zero row (and hence column) sums. There is a one-toone correspondence between the classes of hollow symmetric matrices and centered symmetric matrices, and thus with any hollow symmetric matrix D we may associate a centered symmetric matrix B, and vice...

Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions

Siao Hong, Shuangnian Hu, Shaofang Hong (2016)

Open Mathematics

Let f be an arithmetic function and S = {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj)) (resp. (f[xi, xj])) we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj) (resp. the least common multiple [xi, xj]) of x, and xj as its (i, j)-entry, respectively. The set S is said to be gcd closed if (xi, xj) ∈ S for 1 ≤ i, j ≤ n. In this paper, we give formulas for the determinants of the matrices (f(xi, xj)) and (f[xi, xj]) if S consists of multiple coprime...

Multiscale analysis of wave propagation in random media. Application to correlation-based imaging

Josselin Garnier (2013/2014)

Séminaire Laurent Schwartz — EDP et applications

We consider sensor array imaging with the purpose to image reflectors embedded in a medium. Array imaging consists in two steps. In the first step waves emitted by an array of sources probe the medium to be imaged and are recorded by an array of receivers. In the second step the recorded signals are processed to form an image of the medium. Array imaging in a scattering medium is limited because coherent signals recorded at the receiver array and coming from a reflector to be imaged are weak and...

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