eigenvalues of an involution
Proof. For the first claim suppose is an eigenvalue corresponding to an eigenvector of . That is, . Then , so . As an eigenvector, is non-zero, and . Now property (1) follows since the determinant is the product of the eigenvalues. For property (2), suppose that , where and are as above. Taking the determinant of both sides, and using part (1), and the properties of the determinant, yields
Property (2) follows.
|Title||eigenvalues of an involution|
|Date of creation||2013-03-22 13:38:57|
|Last modified on||2013-03-22 13:38:57|
|Last modified by||Koro (127)|