The rank identities and its applications about the product and sum of three matrices on arbitrary division ring

摘要

Based on the rank identities of the product and sum of three matrices on arbitrary division ring obtained by the block elementary transformation, we prove the rank identity about idempotent matrices A, B still holds under the more weak conditions A2 = A or B2 = B, which rank identity is derived by Y.Liu and C. G. Cao recently, thus improve the corresponding results on the complex number field of Y. Tian and Styan.