The inverse tangent law for the solutions of systems of linear algebraic equations with independent random coefficients is proven under Linderberg's condition.
The system of linear algebraic equations \[ \Xi_{n\times n}\vec x_n=\vec \eta_n, \] where \(n=1,2,\dots ,\;\) \(\Xi_{n\times n}=\bigl[\xi_{ij}^{(n)}\bigr]_{i,j=1,\dots n}\), \(\vec \eta_n^{\top}=\{\eta_i^{(n)} : i=1,\dots,n\}\), \(\vec x_n^{\top}=\{x_i^{(n)} : i=1,\dots, n\}\) with independent random coefficients is considered. The inverse tangent law for such a system is proved under the Lindeberg's condition. The paper is a continuation and generalization of previous results of the first author, (see for example [Random Oper. Stoch. Equ. 19, No. 4, 299--312 (2011; Zbl 1268.60005)]).
scientific article; zbMATH DE number 6881624