Does $AB$ and $BA$ have the same 'number' of each non-zero eigenvalue?
99585
Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?
95227
Is the set of all $n\times n$ matrices, such that for a fixed matrix B  AB=BA, a subspace of the vector space of all $n\times n$ matrices?
110502
$AB=BA$ with same eigenvector matrix
81070
Why must the eigenvalue of the number operator be an integer?
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
50384
A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum
149923
eigenvalues of A - aI in terms of eigenvalues of A
150376
Does Real Eigenvalues mean it is an hermitian Matrix
3301
If $AB = I$ then $BA = I$
85167
When A and B are of different order given the $\det(AB)$,then calculate $\det(BA)$
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 $YX$
45527
Do real matrices always have real eigenvalues?
120687
If the sum of eigenvectors is an eigenvector, then they all correspond to the same eigenvalue
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
128453
If $A$ has two eigenvalues $\lambda _1, \lambda_2$ and $\dim (E_{\lambda_1})=n-1$, then $A$ is diagonalizable