The semidefinite matrix rank minimization, which has a broad range of applications in system control, statistics, network localization, econometrics and so on, is computationally NPhard in general due to the noncontinuous and non-convex rank function. A natural way to handle this type of problems is to substitute the rank function into some tractable surrogates, most popular ones of which inclu...

To every infinite lower Hessenberg matrix D is associated a linear operator on l2. In this paper we prove the similarity of the operator D − ∆, where ∆ belongs to a certain class of compact operators, to the operator D−∆′, where ∆′ is of rank one. We first consider the case when ∆ is lower triangular and has finite rank; then we extend this to ∆ of infinite rank assuming that D is bounded. In S...

The semidefinite matrix rank minimization, which has a broad range of applications in system control, statistics, network localization, econometrics and so on, is computationally NPhard in general due to the noncontinuous and non-convex rank function. A natural way to handle this type of problems is to substitute the rank function into some tractable surrogates, most popular ones of which inclu...

One of the most important prediction problems in finite population is the prediction of a linear function of characteristic values of a finite population. In this paper the admissibility of linear predictors of an arbitrary linear function of characteristic values in a finite population under reflected normal loss function is considered. Under the super-population model, we obtain the condition...

Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.