Source for if $L_A:(\mathbb{R}^n, \left\Vert \cdot \right\Vert_p) \to (\mathbb{R}^n, \left\Vert \cdot \right\Vert_q)$ is an isometry, then $p = q$.
41846
$(\mathbb{R}^n,\|\cdot\|_{p})$ is isometrically isomorphic to $(\mathbb{R}^n,\|\cdot\|_{q})$ iff $p=q,$
47031
Isometric to Dual implies Hilbertable?
44447
Isometry from Manhattan plane to Euclidean plane?
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
39763
Proving left-invariance (and proof-verification for right-invariance) for metric constructed from left-invariant Haar measure
27517
Isometry in compact metric spaces
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
145462
On the canonical isomorphism between $V$ and $V^{**}$
89533
$\mathcal{K}(L^2(\mathbb{R}^m \times \mathbb{R}^n)) = \mathcal{K}(L^2(\mathbb{R}^m)) \otimes \mathcal{K}(L^2(\mathbb{R}^n))$?
144382
Proving $\lVert x \rVert_3$ is smaller than euclidean norm
52556
Isomorphism of $S^1$.
63845
Diffeomorphism $f:U\to V$ then $Df:\mathbb{R^n}\to\mathbb{R^m}$ will be linear isomorphism hence $n=m$
70620
From $n=2$ to $n$-ary Euclid lemma $\ p\mid a_1\cdots a_n\Rightarrow\ p\mid a_1\,$ or $\,\cdots\, p\mid a_n$
75059
Let $T:\mathbb{R}^n\to \mathbb{R}^n$ be a linear transformation...
119247
Let $(M,d)$ be a compact metric space and $f:M \to M$ such that $d(f(x),f(y)) \ge d(x,y) , \forall x,y \in M$ , then $f$ is isometry?
158078
Is linear surjective isometry always unitary?
73790
Are two Hilbert spaces with the same algebraic dimension (their Hamel bases have the same cardinality) isomorphic?