Matrices with a transitive graph and inverse M-matrices

Hadamard Functions of Inverse M-Matrices

We prove that the class of GUM matrices is the largest class of bi-potential matrices stable under Hadamard increasing functions. We also show that any power α ≥ 1, in the sense of Hadamard functions, of an inverseM -matrix is also inverseM matrix showing a conjecture stated in Neumann [15]. We study the class of filtered matrices, which include naturally the GUM matrices, and present some suff...

On Generalized Transitive Matrices

Transitivity of generalized fuzzy matrices over a special type of semiring is considered. The semiring is called incline algebra which generalizes Boolean algebra, fuzzy algebra, and distributive lattice. This paper studies the transitive incline matrices in detail. The transitive closure of an incline matrix is studied, and the convergence for powers of transitive incline matrices is considere...

Z{matrices and Inverse Z{matrices

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, inver...

Inverse Young inequality in quaternion matrices

Inverse Young inequality asserts that if $nu >1$, then $|zw|ge nu|z|^{frac{1}{nu}}+(1-nu)|w|^{frac{1}{1-nu}}$, for all complex numbers $z$ and $w$, and equality holds if and only if $|z|^{frac{1}{nu}}=|w|^{frac{1}{1-nu}}$. In this paper the complex representation of quaternion matrices is applied to establish the inverse Young inequality for matrices of quaternions. Moreover, a necessary and ...

Two modified Jacobi methods for M-matrices