If $(V,\|\cdot \|)$ is a finite dimensional space, then all norms are equivalent.
37924
Equivalence of norms proof
150885
$v \otimes v' = v' \otimes v$ implies $v = av'$
91173
Finite-dimensional subspace normed vector space is closed
129549
Showing that the orthogonal projection in a Hilbert space is compact iff the subspace is finite dimensional
62077
Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
149664
Norm is sup of inner products (proof).
150287
Spectral radii and norms of similar elements in a C*-algebra: $\|bab^{-1}\|<1$ if $b=(\sum_{n=0}^\infty (a^*)^n a^n)^{1/2}$
131993
Prove that vector space and dual space have same dimension
144112
Show that $c_0$ is a Banach space with the norm $\rVert \cdot \lVert_\infty$
78191
Define $\|\cdot\| \colon V \rightarrow \mathbb{R} $ by $\|a\| =\sum 2^n |a_n| $, then choose the correct option
140813
How do i prove that continuous linear transformation between normed spaces is bounded?
150572
Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$
63032
Why is it true that every finite-dimensional inner product space is a Hilbert space?
158706
How convergence relates to equivalence of norms
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
50160
The quotient norm on $\ell^{\infty}(\mathbb{N}) / c_0 (\mathbb{N})$ is given by $\limsup_{n \in \mathbb{N}} |x_n|$.
49087
Show that a norm on an inner product space satisfies parallelogram law.