How to show that $(\operatorname{Im}{A})^⊥ = \ker(A^⊤)$, $\operatorname{Im}{(A^⊤)}= (\ker A)^⊥$?
15793
Is the formula $(\text{ker }A)^\perp=\text{im }A^T$ necessarily true?
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
54099
What are the eigenvalues of $\operatorname{ad}x$?
34702
Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
156858
Kernel of powers of a normal operator
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
128673
Given $A : \mathcal{C} \rightarrow \mathcal{E}$, when does $\operatorname{colim} A = A(1)$?
55488
Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
126018
Show that $ e^{A+B}=e^A e^B$
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
14161
Proof of when is $A=X^TX$ invertible?
2635
equality of two operators...
131844
When does $(e^a)^b = e^{ab}$ hold?
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$