Several equivalent conditions for the reverse order law (ab) = b†(a†abb†)†a† in rings with involution are presented. Also, we investigate necessary and sufficient conditions for (ab) = b†a† to hold.

When improving results about generalized inverses, the aim often is to do this in most general setting possible by eliminating superfluous assumptions and simplifying some of conditions statements. In paper, we use Hartwig’s well-known triple reverse order law as an example for showing how can be done using a recent framework algebraic proofs software package OperatorGB. Our improvements result...

Law and order denotes a negative form of peace secured among the members given social or political order. Minimally, it is an appeal to restore public conditions classed as disorderly, defend against potential articulated threats. But what counts disorder, why problem for any order? Although scientists tend concur that determined by tradition convention, some, fact disorder sufficient them back...

at a superficial level it seems that owning a monopolistic right is in contrast with competitiveness of the market, and exercising this right will prevent the free trade from being competitive. but the truth is that the existence of monopoly is not always a violation of competition law to be harmful to the trade, quite the reverse, in some cases it interacts with principles of competition law, ...

In this article a fast computational method is provided in order to calculate the Moore-Penrose inverse of full rank m× n matrices and of square matrices with at least one zero row or column. Sufficient conditions are also given for special type products of square matrices so that the reverse order law for the Moore-Penrose inverse is satisfied.