- #1
noon0788
- 22
- 0
Hey, I'm wondering if I have a known set of eigenvalues (-1, +1, 0) for A, if I can prove that the matrix A = A3?
I can prove that if A3 = A, that the eigenvalues would be −1, +1, and 0. The following is the proof:
A*k=lambda*k
A3*k=lambda3*k
Since A=A3, A*k=A3*k
lambda*k=lambda3*k
lambda*k - lambda3*k = 0
lambda - lambda3 = 0
lambda*(1-lambda2) = 0
lambda = 0, -1, +1
Is there any way to prove it the other way around? If I know that the eigenvalues are 0, -1, and +1, can I prove that A3 = A?
Thanks!
I can prove that if A3 = A, that the eigenvalues would be −1, +1, and 0. The following is the proof:
A*k=lambda*k
A3*k=lambda3*k
Since A=A3, A*k=A3*k
lambda*k=lambda3*k
lambda*k - lambda3*k = 0
lambda - lambda3 = 0
lambda*(1-lambda2) = 0
lambda = 0, -1, +1
Is there any way to prove it the other way around? If I know that the eigenvalues are 0, -1, and +1, can I prove that A3 = A?
Thanks!