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 RAR = 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 R1 and R2 are n × n involutory matrices, then there is a simple bijection between the set of all centro-invertible matrices with respect to R1 and the set with respect to R2.We sincerely thank the referees, whose helpful remarks have improved this manuscript. This work was partially supported by Ministry of Education (DGI Grant MTM2010-18228).Lebtahi Ep-Kadi-Hahifi, L.; Romero Martínez, JO.; Thome, N. (2014). Generalized centro-invertible matrices with applications. Applied Mathematics Letters. 38:106-109. https://doi.org/10.1016/j.aml.2014.07.0081061093