If $S,T$ are mappings from $V \rightarrow V$, where V is finite, then $Rank(S+T) \leq Rank(S) + Rank(T)$
43000
Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$
110381
Prove that if rank(A + B) = rank(A) + rank(B), then col(A) ∩ col(B) = {0}
61066
Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
44069
Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
43907
Contraction mapping in the context of $f(x_n)=x_{n+1}$.
62303
For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
49242
stab(S) is isomorphic to $ S_k \times S_{n-k} $
137093
What is the codimension of matrices of rank $r$ as a manifold?
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
132595
$\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
155621
Finiteness of the dimension of a normed space and compactness
62711
Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism