Generalized centro-invertible matrices with applications

Centro-invertible matrices are introduced by R.S. Wikramaratna in 2008. For an involutory matrix R , we define the generalized centro-invertible matrices with respect to R to be those matrices A such that R A R = 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 R 1 and R 2 are n × n involutory matrices, then there is a simple bijection between the set of all centro-invertible matrices with respect to R 1 and the set with respect to R 2 .