Eigenvalues of a 2 × 2 matrix A such that A 2 = II have...
oxidricasbt7
Answered
2022-12-20
Eigenvalues of a matrix A such that I have no idea where to begin. I know there are a few matrices that support this claim, will they all have the same eigenvalues?
Answer & Explanation
Kendall Cortez
Expert
2022-12-21Added 4 answers
If v is an eigenvector of A with eigenvalue , then
Thus, if is an eigenvalue of A and then . This gives only two possibilities for , . Notice, that we never assumed that A is . Indeed, if A is any square matrix and then the only possible eigenvalues of A are .