In this paper we study the characteristics of matrices that commute with a given matrix A It appears that these are related to the null space of a well structured matrix More precisely any matrix R that commutes with A has its vectorized column in the null space of that well structured matrix Hence the problem of nding such matrix R is equivalent to that of obtaining a representation of a basis...

Consistency and realness have always been the two critical issues of image super-resolution. While has dramatically improved with use GAN prior, state-of-the-art methods still suffer inconsistencies in local structures colors (e.g., tooth eyes). In this paper, we show that these can be analytically eliminated by learning only null-space component while fixing range-space part. Further, design a...