characteristic root
nounEtymology Calque of French racine caractéristique, the term preferred by French mathematician Augustin-Louis Cauchy (1789–1857).
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Linear algebra, Mathematics, Sciences 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.
- The determinant of a matrix is the product of its characteristic roots.1985, Takeshi Amemiya, Advanced Econometrics, Harvard University Press, page 459:
1 more example
- 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