Suppose that $A$ is a normal matrix. Prove that one can write: $A = G^4$ for some self-adjoint matrix $G$
140400
Prove normal matrix is 4th power of some self-adjoint matrix
80186
How to show that $K\leq S_4$ is a normal subgroup?
21217
$G$, group. $a,b\in G$. Show that $|a|=|a^{-1}|; |ab|=|ba|$, and $|a|=|cac^{-1}|, \forall c\in G$.
110086
Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues
112701
Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
133036
Jordan normal form and invertible matrix of generalized eigenvectors proof
17430
If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ prove that $\det(AD)=\det(BC)$
99942
A normal, idempotent linear operator must be self-adjoint
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
37162
Prove that matrices have equal rank.
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
134306
If $A$ is a normal matrix such that $A^{247} = A^{246}$, how to prove that $A$ is an orthogonal projection?
50404
How to prove a matrix is nilpotent?
16804
Prove whether or not a subgroup is normal in the dihedral group $D_4$
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
28108
Proving the kernel is a normal subgroup.
6169
If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$