If any two norms on a vector space are equivalent then the space is finite-dimensional
18195
Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces
77036
Normed vector spaces over finite fields
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
59697
Is the boundary of the unit sphere in every normed vector space compact?
20921
If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \leq A \leq B$, then det $A \leq$ det $B$.
62425
Equivalent Definitions of the Operator Norm
57619
Norms Induced by Inner Products and the Parallelogram Law
59803
Converse of Schur's Lemma in finite dimensional vector spaces
149664
Norm is sup of inner products (proof).
112548
Existence of non-trivial linear functional on any vector space
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
91173
Finite-dimensional subspace normed vector space is closed
10383
The $ l^{\infty} $-norm is equal to the limit of the $ l^{p} $-norms.
81379
Any two bases of a finite dimensional vector space must have the same number of elements.
145535
Product norm on infinite product space
152325
Every subspace of the dual of a finite-dimensional vector space is an annihilator
83054
Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional