$Rank(A+B)\leq Rank(A)+Rank(B)$
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
116389
If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute
64955
Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
17430
If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ prove that $\det(AD)=\det(BC)$
112676
Inequality $(a+b+c)(ab+bc+ca)(a^3+b^3+c^3)\le (a^2+b^2+c^2)^3$
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
5222
$\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$
97487
How to prove whether a matrix has rank $1$
154085
$\sum a_i \ln(b_i) \leq \sum a_i \ln(a_i)$ with $\sum a_i = \sum b_i = 1$
67784
If $A + A^t = 2I$ then $\det(A) \geq 1$
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
139743
Necessary condition for have same rank
134402
$\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
133870
if $\alpha\leq\beta$ then there is $\gamma$ such as $\alpha+\gamma=\beta$
3109
Prove that $(p+q)^m \leq p^m+q^m$