# All Questions

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### Find the limit of this example?

Please, can you help me to find the limit of the example where n goes to infinity ?
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### A vector space with topology generated by a family of typologies each makes it a topological vector space is a topological vector space

Let $V$ be a vector space, and let $(\mathcal F_ \alpha ) _{ \alpha \in A}$ be a family of topologies on V, each of which turning $V$ into a topological vector space. Let $\mathcal F$ be the vector ...
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### Sufficient statistic of a geometric rv

Can anyone help me prove the sufficient statistics of geo r.v. I am stuck and cant cancel out the thetaws . thanks.
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### What is a way to smoothly convert a number from 0 to 100 to a number from 0 to 7, with 1.75 as the midpoint?

I am working on a problem for some animation software I am writing. I came up with this function, working backward from a graph: $0.8733\cdot \arctan \left(x^a\cdot -2.1855\right)+1$ The graph is ...
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### Proving the equality of two linear maps, using the linear operator

Suppose $W$ is a finite dimensional vector space and $T_1,T_2$ are linear maps from $V$ to $W$. Show that $null$ $T_1 \subset$ $null$ $T_2$ if and only if there exists $S \in L(W, W)$ such that $T_2$ ...
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### Intuition for “the existence of a basis for every vector space is equivalent to the Axiom of Choice”?

Is there a intuitive way to understand "the existence of a basis for every vector space is equivalent to the Axiom of Choice"?
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### Why do people look into modules over Dedekind domains?

It is said in this blog that: The reason this turns out to be useful is that many examples in algebraic/arithmetic geometry require you to look no further than understanding modules over Dedekind ...
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### Algebraic numbers and their minimal polynomials

Obviously, algebraic numbers uniquely determine their minimal polynomials but not the other way around. But, in general, what is the worst case scenario- if given a minimal (irreducible, monic, of ...
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### Is the product of three positive semidefinite matrices positive semidefinite

Is the product of three positive semidefinite matrices positive semidefinite if the product is symmetry? If so, any proof or reference? Thanks Paper - on weakly positive matrices, from Wigner 1963, ...
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