Prove commuting matrices have the same eigenvectors.
93531
Do commuting matrices share the same eigenvectors?
133036
Jordan normal form and invertible matrix of generalized eigenvectors proof
71203
Proving that two systems of linear equations are equivalent if they have the same solutions
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?
64395
If $v_1,...,v_r$ are eigenvectors that correspond to distinct eigenvalues, then they are linearly independent.
35801
Traceless matrices and commutators
157246
Adjoint matrix eigenvalues and eigenvectors
106097
Spectrum of the sum of two commuting matrices
109471
The eigenvectors of the transpose operator
38945
On the proof that the product of diagonal matrices is a diagonal matrix?
39112
Does a correlation matrix of two variables always have the same eigenvectors?
15417
Tricky problem on skew-symmetric matrices
130498
Linear algebra proof regarding matrices
5616
How can I prove the IFF condition for this group of matrices?
30882
Proving Invertibility and Eigenvalues
90576
Symmetric matrix eigenvalues
87136
All matrices which commute with all $2\times 2$ matrices