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Relation between power trace and determinant of the square matrix. (Chinese. English summary) Zbl 1438.15014
Summary: The Newton formula was applied to solve the problem of computation of traces and determinant of the power matrix. The promotion of the Vieta theorem as a bridge cleverly linked traces of the power square of matrix to its eigenvalues which were taken as an elementary symmetric polynomial group. The relationship between the sum of power square and elementary symmetric polynomial called the Newton formula solved the universal computation problem above. The Newton formula also solved the inverse problem: the eigenvalues of a matrix $$A$$ of order $$n$$ compound known for its eigenpolynomial and $${\mathrm{tr}}{A^k}$$ were computed.
##### MSC:
 15A15 Determinants, permanents, traces, other special matrix functions 15A18 Eigenvalues, singular values, and eigenvectors
##### Keywords:
sum of power square; symmetric polynomial; trace; Newton formula
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