Prove: $\operatorname{rank} A \leq 1$ iff $A=xy^T$ for some $x,y \in \mathbb{R}^{n \times 1}$.
34043
A rank-one matrix is the product of two vectors
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
7775
Show that $|x-y|\leq |x|+|y|$.
28822
$|x| - |y| \leq |x-y|?$
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
94383
Prove that $A^TD-C^TB=I$
156877
Rank-one perturbation proof
126032
Proving a certain inequality
19804
How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
1478
An inequality for powers of reals: $a^{1/n}-b^{1/n}<(a-b)^{1/n}$
55488
Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
122944
Prove $|y''(x)| \leq 40$ for all $x \in [1,3]$.
20626
Prove that $x^y < y^x$
65062
Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$