# All Questions

1answer
23 views

### Matrix which has every vector in the space as an eigenvector is square, diagonal.

I've been trying to solve this linear algebra problem for some time and have gotten stuck. I've been asked to either prove or disprove the following statement: For $V$ an $\mathbb{ R }$ vector ...
0answers
25 views

### $f_x(y) = f(y-x)$, $L^p(\mathbb{R}^n)$ [on hold]

Let $x \in \mathbb{R}^n$ and $f \in L^p(\mathbb{R}^n)$, $f_x$ function on $\mathbb{R}^n$ defines $f_x(y) = f(y-x)$.Let fix $f$ and $1 \leq p < \infty$. Prove that is mapping $x \mapsto f_x$ ...
0answers
28 views

1answer
32 views

### Finding the area of an equilateral triangle on an ellipse

The question is as follows: Let $E$ be an ellipse with major axis length $4$ and minor axis length $2$. Inscribed an equilateral triangle $ABC$ in $E$ such that $A$ lies on the minor axis and $BC$ is ...
0answers
26 views

### Best algebra text for Model Theory

I'm looking for an algebra book that is tailored towards some of the ideas in Model Theory, I'm currently slogging through Hodges' Model Theory. I'm a bit rusty with my algebra and was curious if ...
0answers
10 views

### Topologizing $\mathcal{L}(\mathcal{H}) / \mathcal{S}^p(\mathcal{H})$

Given a separable Hilbert space $\mathcal{H}$ I would like to know how one could topologize the quotient algebra $\mathcal{L}(\mathcal{H}) / \mathcal{S}^p(\mathcal{H})$? Here ...
3answers
35 views

### Proof for complex numbers and square root

Use the polar form of complex numbers to show that every complex number $z\neq0$ has two square roots. I know the polar form is $z=r(\cos(\alpha)+i \sin(\alpha))$. I'm just not sure how to do this ...
1answer
41 views

### Taylor Series Theorem

So I see the argument presented in taylor series, that $$\sum c_n (x-a)^n = \sum \frac{f^{(n)}(a)}{n!} (x-a)^n$$ or $c_n = f^{(n)}(a)/n!$ if $x=a$ the question is, since the above only holds when ...
1answer
32 views

### Showing $f_{n} \rightarrow f$ in $L^{1}$ given an integral condition

Let $f_{n}: [0, 1] \rightarrow [0, \infty)$ be a Borel measurable function such that $$\int_{0}^{1}f_{n}(x)\log(2 + f_{n}(x))\, dx < \infty.$$ If $f_{n} \rightarrow f$ Lebesgue almost everywhere. ...
0answers
21 views

### How to research a series, when only some elements are available

I want something like the On-Line Encyclopedia of Integer Sequences, but for series, not sequences. I'd like to know the name of a series, in what natural phenomenon it happens and so on.
1answer
47 views

### Mid level algebra headscratcher. [on hold]

I have 4 numbers. Base = 100 , Start = 0.4 , Count = 4 , Multiplier = 0.64448 I do 100 × 0.4 = 40 Then 4 times: 40 × 0.64448 = 25.7788368 25.7788368 × 0.64448 = 16.61371067 16.61371067 × ...
0answers
19 views

### Proof that Lipshitz function has a primitive

I was doing exercise 5 of this exercise sheet: http://didel.script.univ-paris-diderot.fr/claroline/backends/download.php?url=L1RENi5wZGY%3D&cidReset=true&cidReq=31UKMT42 And I don't know how ...
1answer
20 views

### Gradient of l2 norm squared

Could someone please provide a proof for the following rule: $$\nabla\|x\|_2^2 = 2x$$ I.E. why is the gradient of the $L_2$ norm square of $x$ equal to $2x$? Thanks
0answers
19 views

### A book on analytic geometry

It's easy to find good recommendation for books here for any subject other than analytic geometry ,therefore I'd like to ask for any suggestion of analytic geometry books ,the only charactrestic I'm ...
2answers
19 views

1answer
69 views

### What math have I missed as an Engineeering graduate? [on hold]

To explain, I have a Master's in Engineering from a well known university. We did a wide variety of mathematical topics, vector calc, perturbation methods, numerical methods, linear algebra, discrete ...

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