About Relations between Continuous and Discrete

What is it about?

In this article, properties of matrices describing both rotations of Cartesian coordinate system as well as permutations were analyzed. It was stated that this properties are identical. It means that permutation matrix is also any rotation matrix. Therefore appears the question: what kind of difference or what kind of similarity is between coordinate systems obtained by permutation of axes and by axes rotation described by transposition of permutation matrix. To answer this question all permutations of axes and respective rotations were examined. In both cases identical configuration of coordinate system axes were obtained. This result was generalized to any dimension of space. At the end, it was discussed from several points of view.

Featured Image