prove the following results for the eigenvalues of an $n \times n$ matrix $A$
50384
A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum
144097
eigenvalues and eigenvectors of $vv^T$
134981
Eigenvalues of $L^\dagger L$ are positive
57318
Property of the conjugate transpose matrix with inner product
149916
Minimum eigenvalue and singular value of a square matrix
28584
Eigenvalues and eigenspaces of AB
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?
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
149923
eigenvalues of A - aI in terms of eigenvalues of A
5616
How can I prove the IFF condition for this group of matrices?
126337
Eigenvalues in orthogonal matrices
81275
Eigenvalue Problem -- prove eigenvalue for $A^2 + I$
73952
Upper bound for the sum of absolute values of the eigenvalues
49158
Multiplicity of eigenvalues
135420
Determining eigenvalues, eigenvectors of $A\in \mathbb{R}^{n\times n}(n\geq 2)$.
129977
Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$
157246
Adjoint matrix eigenvalues and eigenvectors