$\operatorname{Im} A = (\operatorname{ker} A^*)^\perp$
15793
Is the formula $(\text{ker }A)^\perp=\text{im }A^T$ necessarily true?
77891
$(U\circ T)^{*} = T^{*}\circ U^{*}$
78575
If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$
80211
Annihilator of quotient module M/IM
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
58741
Operator Exponential $e^A e^B = e^{A+B}$
19946
Let $W$ be a given subspace of $V$ find the orthogonal complement $W^{\perp}$
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
40321
$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
156858
Kernel of powers of a normal operator
45998
The range of $T^*$ is the orthogonal complement of $\ker(T)$
2626
Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
89177
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
55018
Prove that $A^*A + I$ is invertible