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In summary, the conversation discusses a mathematical discovery about using the eigenvalues and eigenvectors of submatrices to solve for the eigenvectors of a larger matrix. This method reduces the complexity of solving for eigenvectors and an example can be found in the graphic provided by the article.

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kith

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This one: https://arxiv.org/abs/1908.03795

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jedishrfu

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It reduces the complexity of eigenvector solving for large matrices but reducing the problem to smaller matrices and using the computed eigenvalues to aid in the solution.

I still haven't seen a numerical example though the graphic in The Atlantic article gives you an example to be completed by the reader.

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The formula for finding eigenvectors from eigenvalues is: **Ax = λx**, where A represents the matrix, λ represents the eigenvalue, and x represents the eigenvector.

Finding eigenvectors from eigenvalues is important because it allows us to understand the behavior of a linear transformation. Eigenvectors are used in various applications such as image processing, data compression, and machine learning.

Eigenvectors and eigenvalues provide information about the magnitude and direction of a transformation. They also help determine the stability and behavior of a system.

To solve for eigenvectors and eigenvalues, we can use various methods such as the power method, inverse iteration, or the QR algorithm. These methods involve finding the characteristic polynomial of the matrix and solving for its roots.

Yes, the formula for finding eigenvectors from eigenvalues can be applied to any square matrix. However, for non-square matrices, we use singular value decomposition to find the eigenvectors and eigenvalues.

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