If $V$ is a finite dimensional with two norms then $\Vert v\Vert_1 \leq c\Vert v\Vert_2 $
37924
Equivalence of norms proof
20844
Relations between p norms
81112
Proving that the dual of the $\mathcal{l}_p$ norm is the $\mathcal{l}_q$ norm.
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
154762
Dual space of a finite dimensional normed space
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 $B$.
83054
Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional
34272
Proving definition of norms induced by vector norms
70415
Comparison between the $\ell_1$ and $\ell_2$ norms
28511
Hypervolume of a $N$-dimensional ball in $p$-norm
88956
For any three vectors $x,y,z\in\mathbb{R}^d$, we have $ \|y-z\|\cdot\|x\|\leq\|x-y\|\cdot\|z\|+\|z-x\|\cdot\|y\|$
50160
The quotient norm on $\ell^{\infty}(\mathbb{N}) / c_0 (\mathbb{N})$ is given by $\limsup_{n \in \mathbb{N}} |x_n|$.
95513
Proving $W$ is a subspace of $P_{2}$
104578
Suppose that $V$ is a vector space, and $W$ is a subspace of $V$. If $V$ is finite dimensional, then prove $W$ too must be finite dimensional.
131998
let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
119479
Derivative with respect to a 2-norm
158399
Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set