Show that the eigenvalues of $A+B$ is the sum of eigenvalues of $A$ and $B$.
106097
Spectrum of the sum of two commuting matrices
80095
Show $|a|+|b|+|c|+|a+b+c| \geq  |a+b|+|b+c|+|c+a|$ for complex $a$, $b$, $c$
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
92300
For positive $a$, $b$, $c$ with $abc=1$, show that $\sum_{cyc}\sqrt{a^2-a+1}\geq a+b+c$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
106986
Eigenvalues of $AB$ and $BA$
60006
Matrix equation: $A−A(A + B)^{−1}A = B−B(A + B)^{−1}B$
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
129977
Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$
128453
If $A$ has two eigenvalues $\lambda _1, \lambda_2$ and $\dim (E_{\lambda_1})=n-1$, then $A$ is diagonalizable
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
50384
A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum
30882
Proving Invertibility and Eigenvalues
49158
Multiplicity of eigenvalues
94424
Matrices and Eigenvalues of Norm
132913
Sum of two eigenvectors for different eigenvalues