A Solution Matrix by IEVP under the Central Principle Submatrix Constraints

The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>n</a:mi><a:mo>×</a:mo><a:mi>n</a:mi></a:math> real matrix <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:mi>P</c:mi></c:math> is called centrosymmetric matrix if <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"><e:mi>P</e:mi><e:mo>=</e:mo><e:mi>R</e:mi><e:mi>P</e:mi><e:mi>R</e:mi><e:mo>,</e:mo></e:math> where <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M4"><g:mi>R</g:mi></g:math> is permutation matrix with ones on cross diagonal (bottom left to top right) and zeroes elsewhere. In this article, the solvability conditions for left and right inverse eigenvalue problem (which is special case of inverse eigenvalue problem) under the submatrix constraint for generalized centrosymmetric matrices are derived, and the general solution is also given. In addition, we provide a feasible algorithm for computing the general solution, which is proved by a numerical example.