characteristic root

English

Etymology

Calque of French racine caractéristique, the term preferred by French mathematician Augustin-Louis Cauchy (1789–1857).

Noun

characteristic root (plural characteristic roots)

1. (linear algebra) An eigenvalue.
   • 1962 [Prentice Hall], Leonard E. Fuller, Basic Matrix Theory, 2017, Dover, page 217,

     There is an important relationship between the characteristic roots of a symmetric matrix and the r and p of the associated quadratic form. It is true that the number of positive characteristic roots is p, whereas the number of nonzero characteristic roots is r.

   • 1985, Takeshi Amemiya, Advanced Econometrics, Harvard University Press, page 459:

     The determinant of a matrix is the product of its characteristic roots.

   • 2009, Babu Ram, Engineering Mathematics, Pearson Education India, page 13.56,

     Theorem 13.54. The characteristic roots of a Hermitian matrix are real.

Related terms

• characteristic polynomial
• characteristic vector