Show that $\operatorname{Spec}k[x_1,x_2,...,x_n]/(x_1^2+\cdots+x_m^2)$ is normal for $\operatorname{char}k\neq 2, n\ge m \ge 3$
54690
Proving normality of affine schemes
108005
A normal divided by $\sqrt{\chi^2(s)/s}$
68211
Characters of Symmetric and Antisymmetric Powers
43913
Prove that if $A^*+A=AA^*$ then $A$ is normal
151520
About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
76100
Showing that $\left\langle a,b \mid abab^{-1}\right\rangle \cong \pi_1(K) \cong \left\langle c,d \mid c^2 d^2 \right\rangle$
81229
Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
80186
How to show that $K\leq S_4$ is a normal subgroup?
147253
Prove for any $K \leq G$, either $K \leq N$ or $KN=G$ and $[K:K \cap N]=p$ where N is normal in G and $[G:N]=p$
158082
Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
151910
Why is $K^{\ast n}$ contained in the norm group?
93596
If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.
157488
Proving that $k[x,y,z]/(xz - (y^2 + 1))$ is a normal ring.
149664
Norm is sup of inner products (proof).
153448
Show that $A\in\mathbb{C}_n$ is normal $\iff$ $tr(A*A) = \sum_{i = 1}^n|\lambda_i|^2$, where $\lambda_1,...,\lambda_n$ are the eigenvalues of $A$.