Encontrados 6 documentos, a visualizar página 1 de 1
The (2,2,0) drazin inverse problem
Patrício, Pedro; Hartwig, Robert E.We consider the additive Drazin problem and we study the existence of the Drazin inverse of a two by two matrix with zero (2,2) entry.
The (2,2,0) group inverse problem
Patrício, Pedro; Hartwig, Robert E.We characterize the existence of the group inverse of a two by two matrix with zero (2,2) entry, over a ring by means of the existence of the inverse of a suitable function of the other three entries. Some special cases are derived.
The link between regularity and strong-pi-regularity
Patrício, Pedro; Hartwig, Robert E.It is shown that if all powers of a ring element $a$ are regular, then $a$ will be strongly-pi-regular exactly when a suitable word in the powers of $a$ and their inner inverses is a unit.
Some additive results on Drazin Inverses
Patrício, Pedro; Hartwig, Robert E.In this paper, some additive results on Drazin inverse of a sum of Drazin invertible elements are derived. Some converse results are also presented.
On Roth's pseudo equivalence over rings
Hartwig, Robert E.; Patrício, PedroThe pseudo-equivalence of a block lower triangular matrix T = [T_{ij}] over a regular ring and its block diagonal matrix D(T) = [T_{ii}] is characterized in terms of suitable Roth consistency conditions. The latter can in turn be expressed in terms of the solvability of certain matrix equations of the form T_{ii}X - YT_{jj} = U_{ij}.
Diagonalizing triangular matrices via orthogonal Pierce decompositions
Hartwig, Robert E.; Patrício, Pedro; Puystjens, RolandA class of sufficient conditions is given to ensure that the sum a+b in a ring R, is equivalent to a sum x + y, which is an orthogonal Pierce decomposition. This is then used to show that a lower triangular matrix, with a regular diagonal is equivalent to its diagonal iff the matrix admits a lower triangular von Neumann inverse.
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