- #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
- Thread starter Stephen Tashi
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The discussion centers on a mathematical discovery related to neutrino oscillations, specifically the use of eigenvalues and eigenvectors of a matrix and its submatrices to simplify the computation of eigenvectors for large matrices. This approach reduces complexity by breaking down the problem into smaller, more manageable parts, leveraging the computed eigenvalues for the overall solution. Although the concept is well-explained, participants note the absence of numerical examples to illustrate the method, despite a graphic in The Atlantic article prompting readers to engage with the material. The conversation references additional resources, including a blog post by Terence Tao that further explores the relationship between eigenvalues and eigenvectors.
- #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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