- #1
charlies1902
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Show that a matrix and its transpose have the same eigenvalues.
I must show that det(A-λI)=det(A^t-λI)
Since det(A)=det(A^t)
→det(A-λI)=det((A-λI)^t)=det(A^t-λI^t)=det(A^t-λI)
Thus, A and A^t have the same eigenvalues.
Is the above enough to prove that a matrix and its transpose have the same eigenvalues or am i missing something?
I must show that det(A-λI)=det(A^t-λI)
Since det(A)=det(A^t)
→det(A-λI)=det((A-λI)^t)=det(A^t-λI^t)=det(A^t-λI)
Thus, A and A^t have the same eigenvalues.
Is the above enough to prove that a matrix and its transpose have the same eigenvalues or am i missing something?