All Questions
1,809 questions with no upvoted or accepted answers
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Orthogonal polynomials of the second kind
Let $L: \mathbb{R}[x] \rightarrow \mathbb{R}$ be a positive definite linear functional and let that $\{s_n\}$ be a positive semi-definite sequence such that $L(x^n)= s_n, n\ge 0.$ Given a positive ...
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-1
votes
1
answer
459
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Orthogonal decomposition of conditional expectations
Suppose I have a random variable $x$ and a set of conditional distributions on $x$. Here is an example where the conditionals are nested:
$$q_1 := E(x|y_1), \quad q_2 := E(x|y_1,y_2),\quad q_3 := E(x|...
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-1
votes
1
answer
293
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spectrum of a special class of tridiagonal matrices
Consider a real and symmetric tridiagonal matrix with zero diagonals and where subdiagonals and superdiagonals are equal to 1 except the (1,2)-th component being equal to $a$, i.e.,
$$\begin{bmatrix}...
- 15
-1
votes
1
answer
200
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Collecting terms of a linear expression with nested sums and combinatorics in coefficients
I need to collect the $\Pr(\cdot)$ terms of the following expression:
$\sum_{m=3}^{n}\frac{g_{m}\left( \cdot \right) }{\left( \sqrt{\theta \left(
1-\theta \right) }\right) ^{m}}\left[ \sum_{j=2}^{m-1}...
-1
votes
1
answer
492
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Upper bound on iterations count for power iteration algorithm
I'm stuck trying to get upper bound on iterations count for power iteration algroithm for finding first eigenvalue of adjacency matrix $A$ given tolerance value. I've tried to figure something out ...
- 89
-1
votes
1
answer
383
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On the permanent dominance conjecture for symmetric group
The Lieb's permanent dominance conjecture states that the expression $$\frac{d_{\chi}^HA}{\chi(e)}\le per(A)$$ holds for all positive semidefinite matrices $A$, where $d_{\chi}^HA=\sum_\limits{\sigma\...
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-2
votes
1
answer
183
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Property of positive semi-definite
Let $A$ is a positive semi-definite matrix like this:
$$ A = \begin{bmatrix}
1 & \alpha_{1,2} & \alpha_{1,3} & \alpha_{1,4}\\
\alpha_{1,2} & 1 & \alpha_{2,3} & \alpha_{2,4}\\
\...
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-2
votes
1
answer
871
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Rank of a random matrix
Let $x$ a random Gaussian vector of size $n$ with i.i.d coefficients $N(0,1)$. Let $J$ a random matrix with i.i.d coefficients $N(0,\sigma^2/n)$ where $\sigma \in [0,1]$. For any integer T>n, define:
$...
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-3
votes
0
answers
139
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A presentation for the group $GL(n,\mathbb{Z}_p)$
Let $n\ge 2$. Let $p$ be a prime and $\mathbb{Z}_p$ denote the finite field with $p$ elements.
I want to know about the presentation for the group $GL(n,\mathbb{Z}_p)$ consisting of its generators and ...
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