Pseudo-Inverses in Associative Rings and Semigroups

The representations of the Drazin inverse of differences of two matrices

“…In particular, if Ind (A) 6 1, then A D is called the group inverse of A and is denoted by A # (see [1,8,11] …”

Multiscale Analysis in Many-Body Systems

“…Now using that the rate of change of the probability is equal to the rate per unit time times 1 τ , reaction (3) leads to the ME where (P (t + τ ) − P (t))/τ is substituted by ∂P (t) ∂t :…”

A note on computational formulas for the Drazin inverse of certain block matrices

“…The Drazin inverse of the sum P + Q was first considered by Drazin in 1958 in [1]. It was proved that…”

“…where k = ind(A), the index of A, is the smallest nonnegative integer for which rank(A k ) = rank(A k+1 ) (see [1]). When ind(A) = 1, the matrix X is called the group inverse of A and denoted by A # .…”