How to show that $\dim\ker(AB) \le \dim \ker A + \dim \ker B $?
10743
$A, B$ are linear map and dim$null(A) = 3$, dim$null(B) = 5$ what about dim$null(AB)$
142097
Finding the dimension of the orthogonal complement
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
9574
How to show that $\det(AB) =\det(A) \det(B)$?
15626
Relations of a~b iff b = ak^2
24072
Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$
6169
If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
88728
Dimensions of vector subspaces in a direct sum are additive
80095
Show $|a|+|b|+|c|+|a+b+c| \geq  |a+b|+|b+c|+|c+a|$ for complex $a$, $b$, $c$
44685
Inner product on $C(\mathbb R)$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
44721
Dimension of Dirac $\gamma$ matrices
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?