| 单词 | characteristic polynomial |
| 释义 | > as lemmascharacteristic polynomial characteristic polynomial n. Mathematics a polynomial that is the determinant of the matrix A − xI (where A is a given square matrix, I is the identity matrix, and x is the scalar variable), its roots being the eigenvalues of the matrix A; cf. characteristic equation n. 6. ΚΠ 1912 G. A. Bliss in Trans. Amer. Math. Soc. 13 136 If the ‘characteristic’ polynomials* f are all of degree one, then their determinant is the resultant R. [Note] *This nomenclature is due to MacMillan. 1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xvii. 379 To find an eigenvector x one must first find a root of the characteristic polynomial of A. 2006 R. Casse Projective Geom. (2009) iv. 72 The matrix A is called the companion matrix of the polynomial λ³ − aλ² −bλ − c, which is also the characteristic polynomial of A. < as lemmas |
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