Theorem: $AB$ and $BA$ have the same non-zero eigenvalues
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
151332
If $A,B$ have eigenvalues $\pm1$, what can I say about the eigenvalues of $AB,BA$?
71040
If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
8920
There exists $C\neq0$ with $CA=BC$ iff $A$ and $B$ have a common eigenvalue
106288
Prove that the eigenvalues of a block matrix are the combined eigenvalues of its blocks
149923
eigenvalues of A - aI in terms of eigenvalues of A
84626
Why in these matrices are $AB=BA$ not equal? What is the logic behind them?
52882
find nonsingular matrices $B$ and $C$ that satisfy $BC+ CB= 0$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
76200
Is the rank of $AB$ always equal to the rank of $BA$?
19649
A question about the proof of "a symmetric matrix has real eigenvalues".
93531
Do commuting matrices share the same eigenvectors?
134981
Eigenvalues of $L^\dagger L$ are positive
80544
Need verification - Prove a Hermitian matrix $(\textbf{A}^\ast = \textbf{A})$ has only real eigenvalues
24454
The relationship between the eigenvalues of matrices $XY$ and $YX$