Show that the rank of $A+B$ is no more than the sum of the ranks of $A$ and $B$
119435
Rank of the difference of matrices
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
45469
If $a_k = \operatorname{rank}(S^k)$, deduce that $a_k - a_{k+1} \geq a_{k+1} - a_{k+2}$
10483
Prove Sylvester rank inequality: $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n$
143130
Proving that the supremum of $(a,b)$ is $b$.
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
23764
Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets
97487
How to prove whether a matrix has rank $1$
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
63958
how to prove this inequality $(ab+bc+ac)^2 ≥ 3abc(a+b+c)$
93427
Show that $\sum_{i=1}^{n} \frac {a_i}{1+a-a_i} + \prod_{i=1}^{n} {(1-a_i)} \leq 1$
83049
Frobenius Inequality Rank
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
20593
Show that if $a \neq b$ and a and b are positive then $\frac{a}{b}+\frac{b}{a}$ is never an integer
37061
The order of $ab$ when $a,b$ commute
14162
How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$