Showing posts with label Recent Questions - Mathematics - Stack Exchange. Show all posts
Showing posts with label Recent Questions - Mathematics - Stack Exchange. Show all posts

I need to find a matrix which would solve for the following: $$\begin{bmatrix}4 & 7\\4 & 2 \end{bmatrix} * \begin{bmatrix}- & -\\- &- \end{bmatrix} = \begin{bmatrix}1 & 0\\0 & 1 \end{bmatrix}$$


I tried using the inverse which gave me $ \begin{bmatrix}\frac{2}{-20} & \frac{-7}{-20}\\\frac{-4}{-20} & \frac{4}{-20} \end{bmatrix} $


Also attempted making $\Bigg [\begin{matrix}4 & 7\\4 & 2 \end{matrix}\Bigg | \begin{matrix}1 & 0\\0 & 1 \end{matrix}\Bigg ]$


which gave me the following: $\Bigg [\begin{matrix}1 & 0\\0 & 1 \end{matrix}\Bigg | \begin{matrix}\frac17 & 0\\\frac1{20} & \frac1{-5} \end{matrix}\Bigg ]$


I am guessing I did something wrong at some step but Cannot seem to figure out where!






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294447/finding-a-two-by-two-matrix-such-that
04:03

Could you please specify hilbert basis of $L^2([-1,1])$? How will be the representation of a function f $\in L^2([-1,1])$ by means of its Fourier series?






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294445/hilbert-basis-of-l2
04:03

Typically, first-order logic is assumed to include an equality relation $=$, even though this is "non-logical," together with some postulates about equality.


Would it also be useful to include an ordered pair function $(*,*)?$ One could assume that $(x,y)=(x',y')$ precisely when $x=x$ and $y=y'$. Or perhaps it would be best to add denumerably many such functions, $(*)$, $(*,*)$, $(*,*,*)$, etc.


The upshot of doing (either) of these is that relations can now all be unary. This would prettify a lot of notation. For instance, the axiom schema of replacement would look much neater.


Thoughts, anyone?






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294443/would-it-also-be-useful-to-include-an-ordered-pair-function-in-first-order-logic
04:03

I have to find the limit of the following:


$$\lim_{x\to\infty}{\frac{(x+1)(x^2+2)...(x^n+n)}{[(nx)^n+1]^{\frac{n+1}{2}}}}$$


I tried to find the logarithm of the upper side and lower side but it didn't work..what shall I do?






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294440/limits-question-help-me-please
04:03

in the paper http://www.fuchs-braun.com/media/dd209bf5c2203a87ffff80a3ffffffef.pdf section 2 ' Hilbert-Polya space' page: 180 the author introduce the Theta series


$$ F(\phi(x))= x^{1/2}\sum_{n=0}^{\infty}\phi (nx) $$ x >0


of course if we take the Mellin transform of this we will get the formula


$$ G(1/2+is)\zeta(1/2+is) $$


$$ G(s)= \int_{0}^{\infty}dtF(\phi(t))t^{s-1} $$


then the author affirms that the function vanishes at the Riemann zeros only


i know all the properties of this function but why does the authoer introduce it ?? he wants to give an spectral interpretation but how does the spectral interpretation appears from this series ??






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294436/theta-series-and-riemann-hypothesis
04:03

In a problem about calculating the Laurent series of an expresion, I'm seeing:


$$\frac{1}{1+\frac{1}{w}}=\sum_{k=0}^\infty \frac{(-1)^k}{w^k}$$ When does that hold? What are the conditions of $1/w$ for that to be true? I guess that in a more general way: $$\sum_{k=0}^\infty (-1)^kz^k=\frac{1}{1+z}$$ Again, what are the conditions on $z$?






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294435/question-about-infinity-sum
04:03

Is there an analytical solution for the average of the positive part of a normal distribution. Say if I draw $M$ samples from a $N(\mu,\sigma)$ and take the average: $\frac{sum(max(x,0))}{M}$, is there a close form solution for this?


Was trying $\int_0^\infty{f(x) x}dx$ and got $\frac{\sigma}{\sqrt{2\pi}}$ but I don't think this is the value I'm looking for.






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294434/mean-of-the-positive-part-of-a-normal-distirbution
04:03

I'm not sure how to clearly express this informally, but


$A$ is a set containing cars, and $B$ is a set containing parts. But it is also so that $A_1$'s $B$ set is not the same set as $A_2$'s $B$ set, etc.


I could also use the following example to explain what I mean; $A$ is set of moms and $B$ are sets of children that a specific mom in the $A$ set has. Lets say $A_1$ is 'Kari' and $A_2$ is 'Lisa', 'Kari' is the mother of 'Karl' & 'Tia', while 'Lisa' is the mother of 'Bill'. The $B$ set does not contain all the children regardless of mother, but each mother has her own $B$ set.


How can I state using something like this using Set Notation ?






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294432/set-in-a-set-notation
04:03

I am reviewing my probability lecture notes and I decided to try and do the exercises that were solved in the lecture.


I tried to solve the following problem, but came up with a different answer than the one given in the lecture, so I suspect I got it wrong.



We draw cards from a deck of cards (with $52$ cards), what is the probability that the first king was drawn at the $n-th$ draw ?



My attempt:


The total number of sequences of $n$ cards is $\binom{52}{n}\cdot n!$ .


There are $\binom{4}{1}$ ways to get the king in the $n-th$ draw.


There are $\binom{52-4}{n-1}\cdot(n-1)!$ sequences of $n-1$ cards with no king in them.


Hence the answer is $$ \frac{\binom{4}{1}\cdot\binom{48}{n-1}\cdot(n-1)!}{\binom{52}{n}\cdot n!} $$


Can someone please help me understand my mistake ?






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294428/what-is-wrong-with-the-following-solution-to-a-basic-combinatorial-type-probabil
04:03

It's an old question, may be from 7th grade, but I am really looking for a good explanation for this question:



A says to B, "I am three times as old as you were, when I was as old as you are". If the sum of their present ages is 60, find the ages of A and B respectively.







via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294427/a-tricky-logical-age-problem
04:03

Is it true that $$F(t) = \int_{K}f(x,t)dx$$ is continuous if $f$ is continuous and $K$ is compact? How to prove this?






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294422/integral-of-a-continuous-function-is-continuous
04:03

How do I prove $f(n)=n \log{\log{n}} \notin \Theta (n^k)$ for any $k$? I have no idea where to start but I tried plotting the graph in Google and noticed that $\log{\log{n}}$ is very close to 0.


But might it be because it doesn't have a lower bound? Cos as $n \rightarrow 0$, $\log{\log{n}} \rightarrow - \infty$






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294420/prove-fn-n-log-logn-notin-theta-nk-for-any-k
04:03

By letting $R$ be any ring I have to show these following equations hold in $R$:


a) $x\cdot 0=0$


b) $0\cdot x=0$


c) $-(-x)=x$


d) $(-x)\cdot(-y)=x\cdot y$


I'm not really looking for the answer just for a hint to get me started. I guess I'm confused on how to show these properties hold within $R$.






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294419/let-r-be-any-ring-prove-that-the-following-equations-must-hold-in-r
04:03

I’d like to present this math problem that I’ve trying to solve… This matter is important because the covariance matrix is widely use and this leads to new interpretations of the cross covariance matrices. Considering the following covariance block matrix :


\begin{equation} M=\begin{bmatrix} S1 &C \\ C^T &S2 \\ \end{bmatrix} \end{equation}


The matrix S1 and S2 are symmetric and positive semi-definite.C is also positive semi-definite 1- I would like to discover the relation between the eigenvector of M and the eigen vectors of S1 and S2. 2- Discover the relation between the eigenvector of the matricez S1,S2 and C. I used the eigendecomposition but it lead to a very complicated expressions… Could you help me suggesting another approach?


I really thank you!


All the best


GoodSpirit






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294418/block-of-a-covariance-matrix
04:03

Find the domain of convergence of :


$\displaystyle\sum_{n=1}^{\infty} \frac{e^{in}}{(z+1)^n} +\sum_{n=0}^{\infty} \frac{(z+1)^n}{e^{\frac{1}{2}+n}}\ \ \ \ (z\in\mathbb{C})$



I've found that it diverges for any complex number $z$, is this correct ?






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294417/complex-series-convergence
04:03

Any manifold is homeomorphic to the disjoint sum of its connected components. Therefore, the full classification of manifolds of dimension 1 reduces to the study of connected manifolds.


Could you please give a proof (sketch) as well or link to a good reference on the subject?






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294413/what-is-the-topological-classification-of-connected-1-manifolds
04:03

I'm trying to work out a simple loop to produce the following results



/*
    keywords = dray aerial COMPACT tailed

    dray aerial compact tailed  0   1   2   3
    dray aerial compact         0   1   2
    dray aerial tailed          0   1   3
    dray compact tailed         0   2   3
    aerial compact tailed       1   2   3
    dray aerial                 0   1
    dray compact                0   2
    dray tailed                 0   3
    aerial compact              1   2
    aerial tailed               1   3
    compact tailed              2   3
    dray                        0
    aerial                      1
    compact                     2
    tailed                      3
*/


So something like:



n = length keywords

loop until something
{
  keys = empty array

  for ( i = 0 to n )
  {
     add to keys ( keywords[i] )
  }
  print keys

  n = length keys - 1
}


but that's far from the right answer and hence this question :)


This question has also been asked under the SO section as it is for PHP and programmers are quite logical too http://stackoverflow.com/questions/14672108/simple-iteration-formula-for-php






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/293549/iteration-problem
04:18

I know that $$S=\{(x,y,z)\in \mathbb R^3: z^2=x^2+y^2\}$$ is not a regular surface, bacause it has a vertex in $(0,0,0)$. But how to show it precisely? Maybe here is usefull the theorem that a regularv surface is locally a graphic of infinite differentiable function of the form $z=f(x,y)$ or $y=g(x,z)$ or $x=h(y,z)$?


Thanks






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/293545/how-to-prove-that-the-set-is-not-a-regular-surface
04:18

hi friends now a days am dealing numerical problem with cubic spline but am little bit confuse while using them because of term spline and b-spline. I just want to know in easy and simple words what is difference between cubic spline and cubic b-spline. ARe these both terms are same or is b-spline is other name of cubic spline..help me






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/293542/cubic-spline-verses-cubic-b-splines
04:18

I am beginner in this subject. I understand at least definition of topology. However, I don't get how Topology: a Set with topology on that Set accounts for shapes. How would you describe the topologically a torus? or Sphere? Is it possible to represent it in the form $(X,S)$, what will $X$ and $S$ be for a torus?


If this question is Not a Real Question, instead of answering, just add a comment, I will delete it.






via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/293540/topology-of-shapes
04:18
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