Identities on the Dimensions of the Spaces for the Linear Mappings over the Skew Field and its Applications

Abstract:

      This paper provides some identities on the dimensions of the image space as well as the null space of the linear mapping over the skew field, and gives se-veral applications involving the rank of a matrix over the skew field , one of the interesting applications is to chavacterize some important matrices by using the identities for the rank of a matrix.