Given A, B, C, and D, block Toeplitz matrices, we will prove the necessary sufficient condition for AB - CD = 0, to be a matrix. In addition, with respect change of basis, characterization normal matrices entries from algebra diagonal is also obtained.

Smith normal form computation has many applications in group theory, module theory and number theory. As the entries of the matrix and of its corresponding transformation matrices can explode during the computation, it is a very difficult problem to compute the Smith normal form of large dense matrices. The computation has two main problems: the high execution time and the memory requirements, ...

Smith normal form computation has many applications in group theory, module theory and number theory. As the entries of the matrix and of its corresponding transformation matrices can explode during the computation, it is a very difficult problem to compute the Smith normal form of large dense matrices. The computation has two main problems: the high execution time and the memory requirements, ...