Prove that $\rho(A+B)\le\rho(A)+\rho(B)$ if $A$ and $B$ commute, where $\rho$ is the spectral radius
73254
spectral radius in normed space is subadditive.
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
25357
Matrices $B$ that commute with every matrix commuting with $A$
101286
How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
63124
Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
128361
The kernel and range of the powers of a self-adjoint operator
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
1932
How to show this equality of $\rho(X,Y)$
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
80009
Prove that $| |a|-|b| | \le |a-b|$
49806
Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
97800
Exterior power "commutes" with direct sum
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
107173
If $a\lt{b}$ and $c\le{d}$, prove that $a+c\lt b+d$