Proving $\dim(R(A)\cap R(B)) \ge \dim(R(AB))$
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
124786
Prove that V contains a subspace of each dimension
76160
Dimension of the sum of two vector subspaces
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
53364
dim$(V)$ = $n$, dim$(W)$ = $m$ $\implies$ dim($L(V,W)$) = $nm$
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
100303
A necessary and sufficient condition for $A\cap(B+C)=(A\cap B)+C$ to hold for submodules
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
102817
$A,B\in M_{n}(\mathbb{R})$ so that $A>0, B>0$, prove that $\det (A+B)>\max (\det(A), \det(B))$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
77192
How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?
84871
Determining the dimension of span$\{AB-BA : A,B \in M_{n \times n}(\mathbb R) \}$
123890
Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
50266
In the following figure prove that: $AK||BC$
103380
Is $\operatorname{height} \mathfrak{p} + \dim A / \mathfrak{p} = \dim A$ true?