All Questions
1,657,336
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Why solve SVD sign ambiguity (indeterminacy) problem choose inner product the singular vector and the individual data vectors?
onsider a matrix A = USV'
A = [1 2;3 4;5 6]
the matrix U is
[-0.23 0.97;-0.97 -0.23;0.06 -0.01]
choose the first column of A as the individual data vector a1 = (1,3,5)
the inner product of u1 is
u1 * ...
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8
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Positive linear functional on $L^{p}$, bounded or not?
Given $0<d<u<1$, define $r=d/u<1$, and $D=\frac{1-d}{d}$. Let $\mathsf{X}
=L^{p}(\mathsf{\Omega},\mathcal{F},\mathrm{P})$, with $1\leq p<\frac{\ln
d}{\ln u}$, $\mathsf{\Omega}=\mathbb{N}...
- 301
-1
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18
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Proof using matrices that the matrix AB-BA=I does not exist
I studied below theorem.
If $A$ and $B$ are two square matrices with real entries, then $AB-BA=I$ has no solutions.
I know that the original proof was a proof using the property $Tr(AB)=Tr(BA)$. ...
- 365
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15
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What is the value that inequality cannot take?
x> 0, y> 0 and z> 0;
$ \frac{5x^{3}yz}{x^{5}+y^{5}+z^{5}}$
Which of the following values cannot the expression take?
A)1 B)2 C)$\sqrt[4]{2}$ D)$\sqrt[5]{25}$ E)$\sqrt[4]{9}$
My approach to ...
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14
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Given that $f(x)=\sum_{n=1}^{\infty} \frac{\sin(nx)}{n^2}$, express the integral $\int_0^1 f(x) dx$ as a series.
Following my last question (Study the uniform convergence of $f (x) = \sum_{n=1}^{\infty} \frac{\sin(nx)}{n^2}$ in $\mathbb{R}$.), the second part of the problem goes as it follwos down below.
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- 123
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7
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Clifford algebra as a functor
Let $F$ be a field s.t. $\operatorname{char} F\neq 2$.
Consider the category $\mathsf{Sym}_F$ (objects — $F$-vector spaces equipped with symmetric bilinear form, morphisms — $F$-linear mapping ...
- 125
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2
answers
29
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Attempt of proving $\frac{\pi^3}{3^\pi} < 1 $ using simple algebra led to contradictory answer
I am trying to prove $\frac{\pi^3}{3^\pi} < 1 $ using simple algebraic manipulation but it yielded the opposite answer(it yielded greater than 1). Every move I made seems correct and yet it yielded ...
1
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14
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Asymptotics of $I_n:=\int_1^\infty \frac{d}{dx} [x^{3/2}\psi ' (x)]x^{-1/4}(\log x)^{2n}$ as $n\to\infty$.
In Section 1.8(3) of the monograph Riemann zeta function, author H. M. Edwards explains that Riemann derived the power series
$$\xi(s)=\sum_{n=0}^\infty a_{2n}\left(s-\frac{1}{2}\right)^{2n}$$
and ...
- 5,542
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1
answer
16
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Show that if $I_C =C \frac{dV_C}{dt}$ and $V_C=\cos(\omega t)$ then $\frac{V_C}{I_C} = \frac{1}{i\omega C}$
A capacitor is a component that fulfills the relationship $I_C(t) = C \frac{\text{d}V_C(t)}{\text{d}t}$. Show that if $V_C(t) = \cos(\omega t)$ then the capacitor's impedance is $Z_C = \frac{V_C}{I_C}=...
- 539
1
vote
2
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38
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Minimum value of $|z^4+z+\frac{1}{2}|$
Let $z$ be a complex number. What is the minimum value of the expression $|z^4+z+\frac{1}{2}|$ for $|z|=1$?
I wanted to explore the long process of considering $z=x+iy$, and substituting to get the ...
- 2,530
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24
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Integrating both sides differential equations
$$5\frac{dx}{dt}=(20-x)(40-x)$$
I understand, that we can treat derivatives as fractions, and arrive at the correct solution. So rearranging,
$$\frac{5}{(20-x)(40-x)}dx=dt$$
However, now I get ...
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25
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how to prove that two line segments are perpendicular
I encountered with a pretty simple geometry problem, but I'm totally stuck. Can somebody help?
Let a quadrilateral $ABCD$ is inscribed in a circle with center $O$.
Two opposite edges $AB$ and $CD$ ...
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24
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Pressure due to weight of a cylinder
Is this easy to compute please?
$$\lim_{\Delta\theta\to 0} \sum_{\theta=-\frac\pi 2}^\frac\pi 2 {\cos\theta\over \Delta\theta}$$
If $\Delta\theta$ was in the numerator, I would simply use an integral, ...
-3
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19
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Solving $y = \frac{t - h\cdot m + c}{m}$ for $m$ [closed]
I haven't done Algebra in a long time. I've been trying to solve this for a couple of hours.
Would someone show me how to solve the equation below for $m$? In other words, I need $m$ to be on one side ...
- 103
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1
answer
16
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Eigenvalues of superoperators and their Choi matrices
It is well known that $\Phi$ is a completely-positive and trace-preserving (CPTP) map if and only if the corresponding Choi matrix $C_\Phi:=\sum_{i,j} E_{i,j}\otimes \Phi(E_{i,j})$ is positive semi-...
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