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In mathematics, a Nekrasov matrix or generalised Nekrasov matrix is a type of diagonally dominant matrix (i.e. one in which the diagonal elements are in some way greater than some function of the non-diagonal elements). Specifically if A is a generalised Nekrasov matrix, its diagonal elements are non-zero and the diagonal elements also satisfy, ${\displaystyle a_{ii}>R_{i}(A)}$ where, ${\displaystyle R_{i}(A)=\sum _{j=1}^{i-1}|a_{ij}|{\frac {R_{j}(A)}{|a_{jj}|}}+\sum _{j=i+1}^{n}|a_{ij}|}$.

References

1. Li, Wen (15 September 1998). "On Nekrasov's matrices". Linear Algebra and Its Applications. 281 (1–3): 87–96. doi:10.1016/S0024-3795(98)10031-9. See definition 2.1

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