$a_k = \mathrm{rank}(A^{k+1}) - \mathrm{rank}(A^k)$ is increasing
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
75117
$\mathrm{rank}(AB-BA)=1$ implies $A$ and $B$ are simultaneously triangularisable
86325
Is an increasing union of subspaces a subspace?
129647
$A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$
10911
$A \in M_{n}(\mathbb{R})$ has inverse if and only if it's rank is n.
38489
Degree of the extension $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$
71639
Proof $(1+1/n)^n$ is an increasing sequence
67199
Isomorphism $H_n(D^n, S^{n - 1};A)$ and $A$
85465
Let $f$ be increasing on $[a,b]$ and $a < x_1 < \dotsb < x_n < b$. Show that $\sum_{k = 1}^n [f(x_k^+) - f(x_k^-)]\leq f(b^-) - f(a^+)$.
156877
Rank-one perturbation proof
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
47323
Show that $\left(1+\frac xk\right)^k$ is monotonically increasing
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$