A few good necessary and sufficient conditions are given by using inner product and length relation for antisymmetric transformation on Euclidean space.
袁晖坪.反对称变换的特征条件[J].重庆工商大学学报(自然科学版),1999,(1): Yuan Huiping. Characteristic Conditions of Antisymmetric Transformation[J]. Journal of Chongqing Technology and Business University(Natural Science Edition),1999,(1):