# Tagged Questions

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### Recovering Spherical Harmonics from Discrete Samples

Consider a collection of $N$ points on the 2-sphere chosen uniformly at random. Let's say that there's an edge between two such vertices if their geodesic distance is less than $r_N$. The resulting ...

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64 views

### interpretation of generalized eigenvalue/vectors in spectral graph theory

Let us say I have a symmetric graph adjacency matrix A, a degree matrix D, a laplacian L (D-A). I have a generalized eigenvalue equation $Av=\lambda Lv$. Does the eigenvalue/vectors produced in this ...

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78 views

### Decay rate of Discrete Prolate Spheroidal Sequences in frequency

What is the decay rate of DPSS sequences in frequency?
Consider an interval $T\subset\mathbb{Z}$ of length N in time. Consider another interval $[-W,W]$ in frequency with $W<1/2$. Let $\phi_0$ ...

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**2**answers

470 views

### Efficiently computing a few localized eigenvectors

Let $H = \triangle + V(x) : \mathbb{R}^2 \rightarrow \mathbb{R}^2$. I am interested in domain decomposition for an eigenproblem involving $H$.
The lowest 1000 eigenfunctions of $H$, $ \psi_i $, can ...

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**3**answers

922 views

### Generalization of eigenvalues/vectors to modules?

What is the generalization of eigenvalues/vectors to modules?
To be specific, given a "vector" v in a module over some ring, and a linear "operator" O from the module to itself (please feel free to ...

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**5**answers

831 views

### Can always a family of symmetric real matrices depending smoothly on a real parameter be diagonalized by smooth similarity transformations?

This question is related to another question, but it is definitely not the same.
Is it always possible to diagonalize (at least locally around each point) a family of symmetric real matrices $A(t)$ ...

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votes

**1**answer

880 views

### dominant eigenvector

Hi, everyone! Is there any efficient way to simplify the following tensor product
$X \otimes X + X^T \otimes X^T$, where $X$ is a square $n \times n$ matrix.
My goal is to efficiently compute the ...

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**2**answers

2k views

### Conditions for smooth dependence of the eigenvalues and eigenvectors of a matrix on a set of parameters

Let $A\in\mathcal M_n$ be an $n\times n$ real [symmetric] matrix which depends smoothly on a [finite] set of parameters, $A=A(\xi_1,\ldots,\xi_k)$. We can view it as a smooth function $A:\mathbb ...