# Tagged Questions

48 views

### $l^r \subset l^p$ and is it even a subspace

It is true that for $r<p$ and $r,p \in [1,\infty)$ we have that $l^r \subset l^p$. Is it true that $l^r$ cannot be isomorphic to a subspace of $l^p$?
12 views

### Is this a subspace of R³?

Is the vector (t,3+t,) a subspace of R³? I know for this you have to test the 3 vector space axioms relating to the zero vector, vector addition and scalar multiplication. I'm just having trouble ...
45 views

39 views

### Proof about non-compact sets and unbounded functions

Let $A \subset \mathbb{R}^n$ be a non-compact subset. Show that there exists a continuous unbounded function on $A$. I have split this into two parts. Either: $A$ is unbounded but closed, or $A$ ...
13 views

### How do I prove that group$B(v) = (x : ||x|| \leq 1)$contains an elipsoid around the axes?

I have no idea on where to begin. Also, I have to prove that the aformentioned set is convex, which I tried by contradicting, and I'm having difficulty with that as well. Any help would be ...
37 views

### Discrepancy over matrix exponential

I am trying to compute $\large e^A$ for $A = \left( \begin{array}{ccc} 0 & a \\ 0 & 0 \end{array} \right)$ Using $\large e^A = \sum \limits_{k=0}^\infty \frac{1}{k!} A^k$ Writing out the ...
21 views

59 views

### Changing variables

If there is a change of variables: $$(\vec x(t),t)\to (\vec u=\vec x+\vec a(t),\,\,\,v=t+b)$$ where $b$ is a constant. Suppose I wish to write the following expression in terms of a gradient in ...
511 views

### Compact set - prove that supremum is actually maximum

There is a compact set $K$ in $\mathbb{R}^n$. The diameter of this set is defined as follows: $D = \sup\limits_{x,\, y\, \in K}\|x-y\|$. I need to prove there are two vectors $a,b$ in $K$ such ...
I am trying to understand when do to line integral and when to do arc length. So I know the formula for arc length varies based on $dx$ or $dy$ like so: $s=\int_a^b \sqrt{1+[f'(x)]^2} \, \mathrm{d} x$ ...
I'm trying to wrap my head around this problem - the interplay between $\nabla$ and $\Delta$ is doing my head in. It says to use the divergence theorem. Prove that \int_\Omega u \cdot \Delta v\, ...