Let σ(A) be the set of all eigenvalues of A. Show that σ(A)=σ(AT) where AT is the transpose matrix of A.
Answer
The matrix (A−λI)T is the same as the matrix (AT−λI), since the identity matrix is symmetric.
Thus:
det(AT−λI)=det((A−λI)T)=det(A−λI)
From this it is obvious that the eigenvalues are the same for both A and AT.
Attribution
Source : Link , Question Author : Zizo , Answer Author : Invisible