SOME INVERSE PROPERTIES OF M-MATRICES AND H-MATRICES - GORMANTARA, JERIKO
Matrix A is called a Z-Matrix if every off-diagonal entries of A is nonpositive. Note that any Z-Matrix A can be written as A = sI ???? B where s > 0 and B is nonnegative matrix. One of interesting subclass of Z-Matrices is the M-Matrices. A Z-Matrix A = sI ???? B is called M-Matrix if s (B) where (B) is the spectral radius of B. One of the well known results is if A ???? I is an M-Matrix, then both A and I ???? A????1 are M-Matrices. A few years later, it is showed that the converse also holds. In this thesis, an analogue of this result for another interesting class, i.e H-Matrix, has been obtained. Matrix A is called an H-Matrix if its comparison matrix is an M-Matrix, where comparison matrix of A = (aij) is a matrix where the diagonal entries are jaiij and the off-diagonal entries are ????jaij j. Finally, some negative results on the classes of group inverse M-Matrices and H-Matrices are presented.