# All Questions

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### Dimension of generalized eigenvector space

From Wikipedia For a matrix A, there may not always exist a full set of linearly independent eigenvectors that form a complete basis – a matrix may not be diagonalizable. This happens when the ...
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### Transform $\; (\lnot q \lor r) \land ( q \lor \lnot r)\;$ into a disjunctive normal form

I was working on an examples from my textbook concerning transforming formulae into disjunctive-normal form (DNF) until I found an expression that I cannot solve. I hope somebody can help me transform ...
270 views

### Proving non satisfiability of the barbers paradox with tableau method

The barbers paradox: In a town there is only one barber. For every man in town, either the barber shaves him or he shaves him self. I need to formalize this: The barber shaves exactely those who ...
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### Derive the expected value for a Pareto distribution?

X is a random value that is Pareto distributed with parameter $a>0$, if $\Pr(X>x)=x^{-a}$ for all $x≥1$. Show that $EX=a/(a-1)$ if $a>1$ and $E(X)=∞$ if $0< a \le1$. I can derive the ...
204 views

### Superball total bounce distance

I am asked to explain how to calculate total bounce distance: A "super" rubber ball is one that is measured to bounce when dropped 70% or higher that the distance from which it is dropped. You are ...
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### If $N$ is normal, show that $\begin{Vmatrix} Nx \end{Vmatrix}$=$\begin{Vmatrix} N^{H}x \end{Vmatrix}$ for every vector $x$

If $N$ is normal, show that $\begin{Vmatrix} Nx \end{Vmatrix}$=$\begin{Vmatrix} N^{H}x \end{Vmatrix}$ for every vector x. Deduce that the ith row of N has the same legth as the ith column. In here, ...
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### Find a diagonal matrix M

Find a diagonal M, made up of 1's and -1's, to show that $A=\begin{pmatrix} 2 & 1 & & \\ 1 & 2 & 1 & \\ & 1 & 2 & 1 \\ & & 1 & 2 \end{pmatrix}$ is ...
186 views

### isomorphism $\Bbb Q$ to $\Bbb Q \cap (0,1)$

I've got a question in my homework: Prove that $\langle \mathbb{Q},< \rangle$ and $\langle \mathbb{Q}\cap (0,1),< \rangle$ are isomorphic. I have tried to find a bijective function without any ...
872 views

### Visualization of Singular Value decomposition of a Symmetric Matrix

The Singular Value Decomposition of a matrix A satisfies $\mathbf A = \mathbf U \mathbf \Sigma \mathbf V^\top$ The visualization of it would look like But when $\mathbf A$ is symmetric we can do: ...
202 views

### Testing a hypothesis with significance level

Prove the hypothesis that the average content of containers of a particular lubricant is $10$ liters, if the contents of a random sample of $10$ containers are: \begin{array}{|c|c|c|c|c|} \hline ...
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### Irrationals can be separable by finding a countable dense subset. [duplicate]

Possible Duplicate: Is the set of irrationals separable as a subspace of the real line? Prove the irrationals are separable directly by finding a countable dense subset.
170 views

### Centre of a quadric

I found the following sentence in my linear linear algebra book (affine and projective geometry): $Q:V \to \mathbb{K}$ is a quadric (quadratic function) and $\alpha\in Aff(V)$. $Aff(V)$ is the set of ...
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### Using combinatorial argument prove that $\frac{(3n)!}{2^n\times 3^n}$ is an integer.

Using combinatorial argument prove that $\frac{(3n)!}{2^n\times 3^n}$ is an integer. If we arrange $3n$ objects where there are 3 objects of one kind, another 3 objects of second kind $\cdots$ ...
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### group law on weil-chatelet group

Is there a reference for the gemetric definition of the group law on the Weil-Châtelet group of an Abelian variety more recent than the original Weil's paper ("On algebraic groups and homogeneous ...
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### What are the advantages of dual of a problem

I am studying linear programming and I came across primal-dual algorithm in Linear Programming. I understood it but I am unable ...
721 views

### probability of choosing the same color twice in 5 tries

I'm sure this question has been asked before but I couldn't find an answer. There are 8 balls: 3 red, 2 blue and 3 black. Whats the probability of choosing at least 2 red balls if we pick 5 balls? I ...
There is a corollary in Rudin analysis. But I am not able to understand it. Can someone help to understand it? The Corollary is: Let $f$ be a real differential function on $[a,b]$, then $f'$ ...
Represent in first order logic "Every person who dislikes all vegetarians is smart" My solution $\forall x,y$ $person(x) \land vegetarian(y) \land dislike(x,y) \rightarrow smart(x)$ People say to ...