A matrix and its transpose have the same set of eigenvalues/other version: AA and ATA^T have the same spectrum

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.


The matrix (AλI)T is the same as the matrix (ATλI), since the identity matrix is symmetric.



From this it is obvious that the eigenvalues are the same for both A and AT.

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