We show that a bounded linear operator A ∈ B(H) is a multiple of a unitary operator if and only if AZ and ZA always have the same numerical radius or the same numerical range for all (rank one) Z ∈ B(H). More generally, for any bounded linear operators A,B ∈ B(H), we show that AZ and ZB always have the same numerical radius (resp., the same numerical range) for all (rank one) Z ∈ B(H) if and on...

Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix M , the goal is to compute a matrix M ′ of given rank r in a linear or affine subspace E of matrices (usually encoding a specific structure) such that the Frobenius distance ‖M −M ′‖ is small. We propose a Newton-like iteration for solving ...

Standard face recognition algorithms that use standard feature extraction techniques always suffer from image performance degradation. Recently, singular value decomposition and low-rank matrix are applied in many applications,including pattern recognition and feature extraction. The main objective of this research is to design an efficient face recognition approach by combining many tech...

In this study, we propose a three-stage weighted sum method for identifying the group ranks of alternatives. In the first stage, a rank matrix, similar to the cross-efficiency matrix, is obtained by computing the individual rank position of each alternative based on importance weights. In the second stage, a secondary goal is defined to limit the vector of weights since the vector of weights ob...

It is shown that for $n \le 3$ the joint numerical range of a family commuting $n\times n$ complex matrices always convex; \ge 4$ there are two whose not convex.