Some applications of canonical forms of real antisymmetric matrices

In the report, a new prove method of the orthogonal canonical form theorem of real antisymmetric matrices was proposed, and some applications of the orthogonal canonical form of real antisymmetric matrices were further studied. Firstly, the centralizer and dimension of the real antisymmetric matrix were obtained; secondly, it was proved that for each positive odd number m, the real antisymmetric matrix has only one m-th root of real antisymmetric matrix; finally, some basic results about real antisymmetric matrices were intuitively solved from the orthogonal canonical form.