characteristic polynomial of a orthogonal matrix is a reciprocal polynomial
Theorem 1.
The characteristic polynomial of a orthogonal matrix
is a reciprocal polynomial
Proof.
Let be the orthogonal matrix, and let be its characteristic polynomial. We wish to prove that
Since , we have
Taking the determinant of both sides, and using
and
(),
yields
∎
References
-
1
H. Eves,
Elementary Matrix
Theory, Dover publications, 1980.
Title | characteristic polynomial of a orthogonal matrix is a reciprocal polynomial |
---|---|
Canonical name | CharacteristicPolynomialOfAOrthogonalMatrixIsAReciprocalPolynomial |
Date of creation | 2013-03-22 15:33:13 |
Last modified on | 2013-03-22 15:33:13 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 5 |
Author | matte (1858) |
Entry type | Theorem |
Classification | msc 15-00 |
Related topic | CharacteristicPolynomialOfASymplecticMatrixIsAReciprocalPolynomial |