# Questions tagged [eigenvalues]

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### Eigenvalues of a matrix sum

I have a control system problem, which ends up in that the eigenvalues of the system matrix should have a negative real part, then the system is stable. The system matrix is real but not symmetric. ...
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### Simple way to calculate the eigenvalues of a $2 \times 2 \times 2$ tensor

I am working with hypergraphs. The various matrices associated with hypergraphs are hypermatrix or tensors. I am interested in spectral aspects. In particular, I want to find all the eigenvalues ...
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### Eigenvalues of adjacency matrix of a k-regular graph

If $A_G$ is the adjacency matrix of a k-regular graph, let $B = J+xA_G$, where J is the matrix whose elements are all 1s and $x\in R$ is a scalar. If $\lambda_1\geq\lambda_2\geq \dots \geq \lambda_n$ ...
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### Perturbation analysis and sensitivity of eigenvector matrix product with specific perturbation

In my research in applied linear algebra and probability (Wiener filtering) I have come across this rather interesting problem: For a matrix $U$ we denote by $U_k$ the matrix formed by taking ...
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### Eigenvalues of an integral operator

Let $K\in L^2((0,1)\times(0,1))$ and consider the operator defined in $L^2(0,1)$ by $$Lu(x):=u(x)-\int_0^1K(s,x)u(s)ds.$$ What kind of assumption might I impose on $K$ such that $\lambda=1$ will be ...
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### Can one Gershgorin circle (only) contain all eigenvalues, when the other circles are not contained in it

In short, following a question from my students, I am trying to find a special case where all the eigenvalues of a matrix lie within only one circle, but not in the others, and the other circles are ...
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### Question about eigenvalues of connectivity matrices for graphs [closed]

I'm a computer science student working on a research project that deals with computational study of atomic clusters. I'm using a graph based representation of the clusters using a binary connectivity ...
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### Is tridiagonal reduction the current best practice to compute eigenvalues of random matrices from the Gaussian ensembles (GOE, GUE, GSE)?

I have tried to compute the eigenvalues of random matrices of the GOE ensemble, using MATLAB. Such matrices of size $n * n$ can be obtained easily, symmetrizing matrices whose elements follow the ...
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### Unimodality of a function of a non-negative matrix

I am taking an interest in the following problem: Consider a real matrix with non-negative entries $\boldsymbol{A} \in \mathbb{R}_+^{d \times d}$, with $d \in \mathbb{N}$. For $k \in \mathbb{N}$, ...
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### When is it possible to find the sum of all elements of inverse of a matrix?

Given sum of elements of each row of a positive definite square matrix $M$ of order $n$ all of whose entries are non-negative, when is it possible to find the sum of all elements of the matrix $M^{-1}$...
Consider the matrix $$A = u_1 v_1^{\top} + u_2 v_2^{\top} + ... + u_n v_n^{\top} \in \mathbb{R}^{m \times m},$$ where $u_i$, $v_i$ $\in \mathbb{R}^{m}$. Are there non-trivial conditions on $n$ ...