Diagonalizable matrices A and B with $\mathrm{Tr}(A^k)=\mathrm{Tr}(B^k)$ have the same characteristic polynomial?
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?
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
6091
Similarity of products $AB$ and $BA$ of square matrices
35247
The characteristic and minimal polynomial of a companion matrix
116820
If two matrices have the same characteristic polynomials, determinant and trace, are they similar?
19280
Jordan Canonical Form determined by characteristic and minimal polynomials in dimension $3$, but not beyond
26801
Show that orthogonal matrices are diagonalizable
33477
Proving that if $A$ is a $8\times 8$ matrix over $\mathbb{R}$ and $A^3=A$, then $A$ is diagonalizable.
21571
Why are real symmetric matrices diagonalizable?
40478
If $C$ commutes with certain matrices $A$ and $B$, why is $C$ a scalar multiple of the identity?
135316
A basic question on diagonalizability of a matrix
133573
characteristic polynomial of the adjacency matrix of a tree
63920
Does the fact that matrices $A, B$ are similar imply that $A+cI$ is similar to $B+cI$?
11566
Similar matrices and minimal polynomial
132213
Is every real monic polynomial the characteristic polynomial of a real matrix?
59055
Diagonalizable transformation restricted to an invariant subspace is diagonalizable
31029
Characteristic polynomial of a matrix of $1$'s