a)Show that for any square matrix A, A^t (A transpose) and A have the same characteristic polynomial and hence the same eigenvalues.
b)Give an example of a 2x2 matrix A for which A^t and A have different eigenspaces.
Thank you.
a)Show that for any square matrix A, A^t (A transpose) and A have the same characteristic polynomial and hence the same eigenvalues.
b)Give an example of a 2x2 matrix A for which A^t and A have different eigenspaces.
Thank you.
would that be sufficient enough to say that since det(A) = det(A^t)
then det(A-xI)=det(A^t-xI) since we pretty much subtract the same number, I also considered this solution except it seemed too short to me to be true?
thanks again