If $AA^*=AA$, how to prove $A$ is an Hermitian?
62030
$A^2=A^*A$. Why is matrix $A$ Hermitian?
131611
$A^TA$ is always a symmetric matrix?
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
37985
Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
157321
Why does the action have to be hermitian?
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
64747
If $A^m=I$ then A is Diagonalizable
43913
Prove that if $A^*+A=AA^*$ then $A$ is normal
131701
Why is $A^TA$ invertible if $A$ has independent columns?
128985
Show that $\langle x,y\rangle_A = \langle Ax,Ay\rangle$ is an inner product on $\mathbb R^n$
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
56943
Normal operator with real spectrum is hermitian.
72046
Prove all eigenvalues of $A^*A$ are non-negative
61538
Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric
34702
Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
71064
How to prove that $\langle Av,w\rangle=\langle v,A^Tw\rangle$?