0 like 0 dislike
66 views
Say $A \in M(n, \mathbb{F})$ has rank $k$. Define
$\mathcal{L}:=\{B \in M(n, \mathbb{F}) \mid B A=0\} \quad \text { and } \quad \mathcal{R}:=\{C \in M(n, \mathbb{F}) \mid A C=0\} .$
Show that $\mathcal{L}$ and $\mathcal{R}$ are linear spaces and compute their dimensions.
| 66 views

0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
1 like 0 dislike