Showing that $M$ and $N$ will have same eigenvalues.
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?
106986
Eigenvalues of $AB$ and $BA$
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
37162
Prove that matrices have equal rank.
33591
Product of two matrices sharing the same eigenvector
30877
How to show that the set of orthogonal n x n matrices forms a group under multiplication
118283
Show that if $A^{n}=I$ then $A$ is diagonalizable.
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
118883
If $\lambda_{max} = n$, then $n\times n$ positive, reciprocal matrix A is consistent
50384
A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum
94424
Matrices and Eigenvalues of Norm
51678
Proof that the largest eigenvalue of a stochastic matrix is $1$
43764
Prove $P_m X P_n$ is Hamiltonian if and only if at least one of $m,n$ is even
129680
Prove that $n$ is even.
35080
If matrices $A$ and $B$ commute, $A$ with distinct eigenvalues, then $B$ is a polynomial in $A$
7457
Prove that $J^+AJ$ has positive eigenvalues
149629
The Eigenvalues of a block matrix