- #1
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Anyone know what result this article is talking about? https://www.theatlantic.com/science...-lead-striking-mathematical-discovery/602128/
What's the formula? - eigenvectors from eigenvalues
- Context: Undergrad
- Thread starter Stephen Tashi
- Start date
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Discussion Overview
The discussion revolves around the mathematical relationship between eigenvalues and eigenvectors, particularly in the context of simplifying the computation of eigenvectors for large matrices by utilizing the eigenvalues and eigenvectors of their submatrices. The scope includes theoretical exploration and references to relevant articles.
Discussion Character
- Exploratory, Technical explanation
Main Points Raised
- One participant references an article discussing a mathematical discovery related to neutrino oscillations and its implications for eigenvalues and eigenvectors.
- Another participant provides a link to a preprint that may contain relevant information on the topic.
- A participant suggests that the eigenvalues of a matrix A, along with the eigenvalues and eigenvectors of its submatrices, can be utilized to compute the eigenvectors of A, potentially simplifying the process for large matrices.
- The same participant notes the absence of a numerical example in the discussion, although a graphic in the referenced article is mentioned as providing an example for readers to complete.
- Additional resources are shared, including a blog post by a mathematician that may elaborate on the topic.
Areas of Agreement / Disagreement
Participants have not reached a consensus, as the discussion includes various references and ideas without a definitive agreement on the implications or applications of the proposed methods.
Contextual Notes
The discussion lacks specific numerical examples and may depend on the definitions and assumptions regarding the matrices involved, which remain unresolved.
- #2
kith
Science Advisor
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This one: https://arxiv.org/abs/1908.03795
- #3
jedishrfu
Mentor
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The idea is that the eigenvalues of a matrix A combined with the eigenvalues and eigenvectors of the submatrices of A can be used to compute the eigenvectors of A.
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.
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.
- #4
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