Show that $\operatorname{rank}(A+B) \leq \operatorname{rank}(A) + \operatorname{rank}(B)$
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
2798
A and B are nxn matrices, $A =B^TB$. Prove that if rank(B)=n, A is pos def, and if rank(B)<b, A is pos semi-def.
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
67058
Prove that $\text{rank}(X^TX)=\text{rank}(X)$
108704
Help with proof of $|x+y| \geq |x|-|y|$
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
69653
Inequality $\left(a-1+\frac{1}b\right)\left(b-1+\frac{1}c\right)\left(c-1+\frac{1}a\right)\leq1$
149287
Prove that $A,B>0$ and $A_{ij}0$
45469
If $a_k = \operatorname{rank}(S^k)$, deduce that $a_k - a_{k+1} \geq a_{k+1} - a_{k+2}$
138036
Proving Inequality using Induction $a^n-b^n \leq na^{n-1}(a-b)$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
145884
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
52204
Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
126032
Proving a certain inequality
64955
Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$