Z{matrices and Inverse Z{matrices
نویسنده
چکیده
We consider Z{matrices and inverse Z{matrices, i.e. those nonsingular matrices, whose inverse is a Z{matrix. Recently Fiedler and Markham introduced a classii-cation of Z{matrices. This classiication directly leads to a classiication of inverse Z{matrices. Among all classes of Z{matrices and inverse Z{matrices the classes of M{matrices, N 0 {matrices, F 0 {matrices and inverse M{matrices, inverse N 0 {matrices and inverse F 0 {matrices respectively, had been studied in detail. Here we discuss each single class of Z{matrices and inverse Z{matrices as well as we consider the whole classes of Z{matrices and inverse Z{matrices. We establish some common properties of the classes like eigenvalue bounds and determinant inequalities and we give a new characterization of all classes of Z{matrices and inverse Z{matrices. Some of the results generalize known results for M{matrices, N 0 {matrices, and F 0 {matrices, and inverse M{matrices, inverse N 0 {matrices, and inverse F 0 {matrices. However, we will also show that some properties of the speciic classes mentioned above do not hold for all classes of Z{matrices and inverse Z{matrices.
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