The aim of this paper is to establish formulae for the Drazin inverse of anti-triangular block matrices under new assumptions in literature. Precisely, we consider the Drazin inverse of three kinds of anti-triangular block matrices. Applying these results, we present new expressions for the Drazin inverse of an arbitrary block matrix. In this way, we generalize a list of earlier results and illustrate it with three examples.
In this paper, we analyze the index relation of anti-triangular block
matrices and their entries to separately obtain new and strict expressions
for the Drazin inverse of them under certain circumstances. As applications,
we utilize the relationship between the anti-triangular block matrix and a 2
? 2 block matrix to establish several formulae. Our results generalize and
unify a series of results in the literature.
:Precision poverty alleviation policy, as a special public policy benefiting some poor people, is essentially fair. Under the background of the widening income gaps in rural areas, the positive role of precise poverty alleviation policy in promoting distribution equity urgently needs to be tested. Using the sample data of 909 rural households in poverty-stricken areas in 2017, this study investigated the impact of precise poverty alleviation policies on distribution equity and its impact mechanism through propensity score matching (PSM) model and ordinary least squares (OLS) model with interactive items. The results show that the precise poverty alleviation policy can effectively improve the disadvantageous position of the poor in income distribution by means of transfer payment and opportunity supply, and greatly improve the sense of fairness in the distribution of the poor. The treatment effects are 4.2% and 0.470, respectively. However, the irrational preference of the poor farmers for transfer payment also arises. Therefore, on the one hand, we should give full play to the governance function of the rural acquaintance society, fully mobilize the poverty-stricken people' s poverty alleviation subjectivity, and improve their irrational preference for transfer payment. On the other hand, we should optimize the distribution structure of poverty alleviation resources and implement differentiated poverty alleviation policies for different types of poverty-stricken families, so as to ensure that precise poverty alleviation policies promote fair distribution and improve the utilization efficiency of poverty alleviation resources.
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