# Questions tagged [eigenvalues]

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values (Hoffman and Kunze 1971), proper values, or latent roots (Marcus and Minc 1988, p. 144).

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### All eigenpairs of large sparse symmetric matrix

In advance I am sorry for my noobish question. I am a physics PHD student and basically I use python for my math/physics problems. But now I have a problem which requires more computing capacity and ...
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### What's the optimal method to solve for the top eigenvectors of a very large, real, symmetric matrix of limited rank?

Consider a real symmetric matrix of dimension N~10^5 and rank m~2000. What is the most efficient algorithm for determining the top m eigenvectors? If the answer isn't obvious, are there existing ...
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### Minimum effort merging of two sets

I have the following problem. I have two sequences of elements $A = [a_1,a_2,\cdots,a_n]$ and $B = [b_1,b_2,\cdots,b_m]$. I can build a matrix $D[n \times m]$ where $d_{ij} = d(a_i,b_j)$ My greedy ...
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### Numerical Stability of a Generalized Spatial Discretization Scheme

After reading the matrix stability chapter (10) of Hirsch [1], I decided to dive in the reference list of the chapter. One of the papers [2], which is cited as reference shows an very interesting ...
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### An Upper Bound of $\left<H,X\right>_F$ with Constrainted Rank

We have $X=[\mathbf{x}_1,\mathbf{x}_2...,\mathbf{x}_n]\in\mathbb{R}^{d\times n}$, $H=[\mathbf{h}_1,\mathbf{h}_2...,\mathbf{h}_n] \in\mathbb{R}^{d\times n}$, and $d<n$. $H$ has rank $r\leq d$ and $X$...
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### LAPACK zlapmt_ freezes code [closed]

I'm using LAPACK's zggev_ routine to solve some generalized eigenvalue problem. While it produces the correct results, I want the eigenvalues and according eigenvectors sorted by absolute value. For ...
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### Examples of finding eigenfunctions of coupled DEs

I am looking for examples of numerically finding eigenvalues/eigenfunctions of coupled DEs. If anyone is able to point me towards any examples, preferably with code included, it would be much ...
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### Boundary conditions generalized eigenvalue problem

Consider the following eigenvalue problem $$\mathcal {L} x(s) = \lambda x(s),$$ where \mathcal {L} = \alpha \partial^4_s + (s^2-1)\partial^2_s + s \...
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### Diagonalize a circulant-plus-rank-one matrix

Suppose $A=uv^T$ where $u$ and $v$ are non-zero column vectors in $\mathbb{R}^n, n\geq 3$. $\lambda=0$ is an eigenvalue of $A$ since $A$ is not of full rank. $\lambda=v^Tu$ is also an eigenvalue of $A$...
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### Most efficient library to diagonalize exactly large hermitian or unitary matrices

I am working on a physics problem which requires obtaining the exact eigenvalues and eigenvectors of Hermitian and Unitary matrices numerically. Naturally I would like to ask the experts what are the ...
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### Are there any constraints on eigenvalues that are used in inverse iteration?

What is the result of the method for multiple eigenvalues? Is there any case for which this method will not work altogether?
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### Armadillo eig_sym() for extracting eigenvalues. Is it parallel at all? [closed]

After wasting 3 days with scalapack, I gave up and moved to Armadillo, considering it uses lapack underneath its beatiful and easy interface. I would like to calculate the eigen values and eigen ...