Volume 23, Issue 4

We study the structure of zero row sum matrices as an algebra and as a Lie algebra in the context of groups preserving a given projection in the algebra of matrices. We find the structure of the Lie algebra of the group that fixes a given projection. Details for the zero row sum matrices are presented. In particular, we find the Levi decomposition and give an explicit unitary equivalence with the affine Lie algebra. An orthonormal basis for zero row sum matrices appears naturally.

We obtain some random fixed point theorems for random mappings. We use the orbits of the random mappings to show the existence of a fixed point for a class of random mappings and also establish the measurability of solutions obtained through such random mappings. Some applications of these theorems to random integral equations are given.

In this paper we apply the REFORM method for the deduction of the system of canonical equations K 60 for normalized spectral functions of the matrices [ A n + B n U n (ε) C n ][ A n + B n U n (ε) C n ] * .

In this paper we apply the REFORM method for the deduction of the system of canonical equations K 61 for normalized spectral functions of the matrices A + B ( U + γ H ) C .