Generalized centro-invertible matrices with applications

Centro-invertible matrices are introduced by R.S. Wikramaratna in 2008. For an involutory matrix RR, we define the generalized centro-invertible matrices with respect to RR to be those matrices AA such that RAR=A−1RAR=A−1. We apply these matrices to a problem in modular arithmetic. Specifically, algorithms for image blurring/deblurring are designed by means of generalized centro-invertible matrices. In addition, if R1R1 and R2R2 are n×nn×n involutory matrices, then there is a simple bijection between the set of all centro-invertible matrices with respect to R1R1 and the set with respect to R2R2.