Show that $ A^* = AU$ for a normal matrix A and a unitary matrix $U$
36771
How to prove that A is normal if and only if there's a unitary matrix V,s.t. A*=AV?
50384
A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum
18585
Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
1865
Sub-determinants of an orthogonal matrix
128985
Show that $\langle x,y\rangle_A = \langle Ax,Ay\rangle$ is an inner product on $\mathbb R^n$
36090
$TT^*=T^2$, show that $T$ is self-adjoint
117175
Proof that the 2-norm of orthogonal transformation of a matrix is invariant
151721
Uhlmann's Theorem: proof of $\text{tr}(A^{\dagger} B) = \langle m | A \otimes B |m\rangle $
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
109736
For a 2x2 matrix A satisfying $A^k=I$, compute $e^A$
126018
Show that $ e^{A+B}=e^A e^B$
26801
Show that orthogonal matrices are diagonalizable
94424
Matrices and Eigenvalues of Norm
126337
Eigenvalues in orthogonal matrices
129977
Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$
4517
Showing a $2\times2$ matrix is invertible
77891
$(U\circ T)^{*} = T^{*}\circ U^{*}$