# Tagged Questions

The process of studying mathematics without formal instruction. _Don't_ use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is _about_.

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### How to decide whether PDE is Homogeneous or non-homogeneous.

I am studying second order PDE. And I have seen homogeneous and non-homogeneous PDE. But I cannot decide which one is homogeneous or non-homogeneous. For examples; (1) $(D^3-3D^2D'+4D'^3)u=0$ ...
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### Complex form of Fourier Series

So, the last part of the university syllabus in the chapter of Fourier Series is: ...
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### Expected value of division

Let $X,Y$ and $Z$ be three indenependent real valued random variables. Al with finite second momennt and all with mean $0$ and variance $1$. Define $$W= \frac{X+YZ}{\sqrt{1+Z^2}}$$ Show that ...
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### Cholesky decomposition: No uniqueness when A is positive semidefinite

I can get as corolary of the following theorem, that Cholesky decomposition is not unique for positive semidefinite matrices? Thank's in advance If $A\in \mathbb{M}_{n\times n}$ is a positive ...
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### Meaning of $E(u|v) = p\,v$

I am having problem understanding the intuition behind this: if $u$ and $v$ are jointly normal (with zero mean), then $E(u|v) = p\,v$, for some parameter $p$ ?
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### Poisson and conditional distribution

Given a source that emits photons let be $X$ the number of photons emitted in $s$ seconds. Let be $p$ the probability that photons reach a detector and let be $Y$ the number of photos that reached the ...
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Now I am just a beginner in commutative algebra, so I just want to ask which book I should read step by step. I am reading Step in commutative algebra of Sharp, then I want to read Commutative ring ...
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### Help needed with partial products

I understand that 4 times 6 tens is 240. I am now being asked to add the extra tens to 240. how do I do that? are the extra tens 40. so if I add 240+40=280 is that the answer?
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### start mathematics from scratch

I'm sorry if this question goes against the site. I have completed my engineering in computer science; we were taught to get degrees only in our university :(. I love mathematics but time passed ...
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### Riesz map between Sobolev space and its dual

I'm asked to find the Riesz's map: $$R:H^1_0(\Omega) \rightarrow H^{-1}(\Omega)$$ $$R: u \mapsto F_u \quad \text{s.t.} \quad <F_u,v>_*= (u_F,v)_{H_0^1} \ \ \forall v \in H_0^1$$ I chose \$(u,...
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### Best Sets of Lecture Notes and Articles

Let me start by apologizing if there is another thread on math.se that subsumes this. I was updating my answer to the question here during which I made the claim that "I spend a lot of time sifting ...
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### Equivalent systems of Linear equation

I've just begun to re-learn linear algebra because is so important, the book that I chose is naturally the Hoffman's for a lot of reason. Well, In the first chapter I'm stuck with the following, ...