Let $A$, $B$ and $C$ be complex matrices such that $C\neq 0, $ $AC=CB$. Prove that $A$ and $B$ have a common eigenvalue.
8920
There exists $C\neq0$ with $CA=BC$ iff $A$ and $B$ have a common eigenvalue
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
40478
If $C$ commutes with certain matrices $A$ and $B$, why is $C$ a scalar multiple of the identity?
87262
How to prove positive semidefiniteness of two matrices through Schur Complement?
41932
Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
82410
Find $C$, if $A=CBC$, where $A$,$B$,$C$ are symmetric matrices.
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
150228
If $E$ has eigenvalues $\lambda_1, \ldots, \lambda_n$, then $B \mapsto [E,B] = EB - BE$ has eigenvalues $\lambda_i - \lambda_j$.
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
140252
Matrices - Conditions for $AB+BA=0$
39779
If $a,b,c>0$ and $a+b+c=1$, prove that $\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ac}{b+ac}} \le \frac{3}{2}$.
129977
Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$
110502
$AB=BA$ with same eigenvector matrix
94424
Matrices and Eigenvalues of Norm
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?