# All Questions

1,086,609 questions
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### Finding Cartesian coordinates of remaining vertices of triangle, given angle from y-axis with point A and a vertex

I have an isosceles triangle ABC, where the height h and angle at point A are known. The Cartesian coordinates of point A are also known. How to find B(x2,y2) and C(x3,y3)? https://i.stack.imgur.com/...
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### General formula for decomposition $n^{th}$ power of $V_1$ rep of $SU(2)$

If $V_n$ is the $n+1$ dimensional irreducible complex rep of $SU(2)$ I'd like to find closed form formula for: $$V_1^{\otimes n}$$ Using tensor distributivity over direct sum and Clebsh formula I'...
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### Is there a product formula for the Bernouilli numbers?

There are many well-known formulas available for the Bernouilli numbers, many of these can be found on the Wikipedia page. However, these are all in the form of infinite sums. I have not found any of ...
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### Conserved quantities for a group action?

I was reading this wiki about moment maps, and they say that moment maps are [...]used to construct conserved quantities for the action What exactly does it mean to be a conserved quantity for an ...
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### The art of proof summarizing. Are there known rules, or is it a purely common sense matter?

When a proof is long and difficult , it can be really nice vis-à-vis the reader to give a summary or an outline of the deduction before beginning hard work. Are there known rules to give a good ...
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### Example of a bilinear form of abelian groups

Let $X$ and $Y$ be abelian groups. Then, a $Y$-valued bilinear form on $X$ is a $\mathbb{Z}$-module homomorphism $$\alpha: X \otimes_{\mathbb{Z}} X \rightarrow Y$$ How does this relate to the standard ...
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### Standard form for the Characteristic Matrix/Polynomial

I'm currently taking Linear Algebra and Differential Equations, and in talking about eigenvalues of a matrix, both professors have given the same information: for some square n x n matrix A, the ...
I´m beginning in the study of Singular Homology using Kosniowski's text. Since it seems that the n-chains group $S_n(X)$ inherites the group structure of $\mathbb{Z}$, we can consider that, in ...
I've been learning about tensor products over modules, but where the ring acting on the module is commutative. When $R$ is non-commutative, we consider a right $R$-module $M$ and a left $R$-module $N$...