Prove that $\text{im}(A^*)=\text{ker}(A)^0$ for a linear transformation $A$
135514
$ \text{range } T' = (\ker T)^0$
44453
Prove that the normalisation of $A=k[X,Y]/(Y^2-X^2-X^3)$ is $k[t]$ where $t=Y/X$ (Reid, Exercise 4.5)
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
120010
Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
35345
How do i prove invertibility of this linear transformation
80544
Need verification - Prove a Hermitian matrix $(\textbf{A}^\ast = \textbf{A})$ has only real eigenvalues
38378
$M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$
76586
How to prove that linear transformations transforms lines into lines
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
34714
What is the relationship between $\ker(A), \ker(A^2), \ldots, \ker(A^n)$?
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
81181
Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
75059
Let $T:\mathbb{R}^n\to \mathbb{R}^n$ be a linear transformation...
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?