M is a square martix, and $φ^*$ : $V^* \to V^*$, then why $M^T=M_{φ^*_M}$?
120399
Transpose matrix dual map
39453
How do I prove that $S^n$ is homeomorphic to $S^m \Rightarrow m=n$?
153355
Given $S \in B(Y^{*}, X^{*})$, does there exist $T\in B(X,Y)$ such that $S=T^{*}$?
146541
Why $\dim U+\dim U^\perp=\dim V$?
33144
Criterion for $\phi(mn)=m\phi(n)$ to be true
57894
In a proof of the Sherman-Morrison formula why does $(I+wv^T)^{-1}=I-\frac{wv^T}{1+v^Tw}$
63845
Diffeomorphism $f:U\to V$ then $Df:\mathbb{R^n}\to\mathbb{R^m}$ will be linear isomorphism hence $n=m$
30178
Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
16420
When does $\sqrt{wz}=\sqrt{w}\sqrt{z}$?
60990
Tricky operator identity: $[L^2,[L^2,\vec{r}]]=2 \hbar ^2 \{ L^2, \vec{r}\}$?
145462
On the canonical isomorphism between $V$ and $V^{**}$
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
141286
When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
158353
If $F=K(u,v)$ with $u^p$,$v^p\in K$ and $[F:K]=p^2$, $\operatorname{char} K=p>0$, then $F$ is not a simple extension of $K$.
71437
How is the derivative of $\textrm{Trace}\left\{ X^T A X B\right\}$ with respect to $X$ equal to $AXB + A^TXB^T$?
24072
Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$
20789
If $\Sigma \vdash \varphi$ then $\Sigma \vdash \forall x \varphi$. Why when $(\varphi \implies \forall x \varphi)$ is not true?