# Questions tagged [eigenvector]

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### On the eigen vectors of a diagonalizable matrix

Let us consider the space $M_n(\mathbb{C})$. By a unitary matrix $U=(u_{ij})$ we mean that $U^{-1}=(\overline{u_{ji}})$. Q. Let $U$ be a unitary matrix. I am looking for the pairs of matrices $(D,A)$ ...
1 vote
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### Find the eigenvectors from the QR algorithm in the unsymmetric case

It is possible to find many references describing the QR Algorithm with more or less refinements to approximate the eigenvalues of a square matrix $A\in\mathbb{R}^{n\times n}$. I implemented a version ...
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### How close to uniform are Perron-Frobenius eigenvectors?

Let $A=(a_{i,j})$ be a square matrix with non-negative entries. (Assume $A$ is symmetric, if it helps.) Let $v$ be a Perron-Frobenius eigenvector. What do we need to assume about $A$ in order to have ...
1 vote
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### When must an eigenvector have only non-negative entries?

What would be a reasonable sufficient condition on a real symmetric matrix that would force its eigenvector with largest eigenvalue (or one of its eigenvectors with maximal eigenvalue) to have only ...
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A symmetric real matrix has interesting properties, for example, its eigenvalues are real and eigenvectors corresponding to distinct eigenvalues, orthogonal. However, in (Pseudo)Riemannian space, if ...
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### Simultaneous diagonalization in Matlab [closed]

Crossposted from StackOverflow. The generalised diagonalization of two matrices $A$ and $B$ can be done in Matlab via [V,D] = eig(A,B); where the columns of $V$ ...
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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 $\lambda_1\geq\lambda_2\geq \dots \geq \lambda_n$ ...