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Tagged with eigenvector laplacian
7 questions
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Eigenvalues and eigenvectors of the path Laplacian
Consider the Laplacian matrix of the path graph:
$$
L = \begin{bmatrix}
1 & -1 & 0 & \cdots & 0 & 0\\
-1 & 2 & -1 & \cdots & 0 & 0\\
0 & -1 & 2 & \...
- 11
2
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1
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220
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Are these the only first eigenfunctions on a hemisphere?
Let $\mathbb{S}^2_+$ denote the closed upper hemisphere of the unit round sphere in $\mathbb{R}^3$. It is well known that the first positive eigenvalue of the Laplacian on the closed unit sphere is $2$...
- 2,095
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Eigenvector to zero eigenvalue of general Laplacian
I was wondering what we can say about the eigenvectors of a matrix $A$ fullfilling $Ax =0$ where $A$ is symmetric with a diagonal equal to one and every row sums up to 0. Obviously this is a ...
1
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2
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153
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From one eigenvector to many, in a very local graph?
Let $\Gamma$ be an undirected graph of bounded degree $d$ with $V = \{1,2,\dotsc,N\}$ as its set of vertices, and edges only between vertices that are at a distance $\leq M$ apart (where $M$ is much ...
- 20.2k
3
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Eigenvectors of graph Laplacian for spectral clustering
I have the following questions regarding the graph Laplacian for spectral clustering:
What is the intuition behind projecting the Laplacian (D-A, where D is the degree matrix and A is the affinity ...
- 31
6
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Density of squares of radial eigenfunctions
The eigenfunctions of the Laplace operator on the disc can be written in polar coordinates as $f(r,\theta)=R_{nk}(r)e^{ik\theta}$, where $k\in\mathbb Z$ and $n\in\mathbb N$ and the radial function is $...
- 8,086
3
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Asymptotic behavior of the Dirichlet-Laplacian eigenvalues [closed]
I found in a math book http://www.cambridge.org/dz/academic/subjects/mathematics/differential-and-integral-equations-dynamical-systems-and-co/introduction-partial-differential-equations?format=PB&...
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