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README.md

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# New Eigenvectors from Eigenvalues Calculation
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This repository implements this new [paper](https://arxiv.org/pdf/1908.03795.pdf) that allows us to calculate eigenvectors from eigenvectors elegantly through PyTorch.
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Full credits given to the **original authors** and the **numpy implementation by Leo Dirac**.
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I ported this to PyTorch as a lot of my workflows are on the GPUs with PyTorch.
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## Run Notebook on Google Colab
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[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ritchieng/eigenvectors-from-eigenvectors/blob/master/notebooks/comparison.ipynb)
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[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ritchieng/eigenvectors-from-eigenvalues/blob/master/notebooks/comparison.ipynb)
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## Authors and Abstract
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PETER B. DENTON, STEPHEN J. PARKE, TERENCE TAO, AND XINING ZHANG
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"We present a new method of succinctly determining eigenvectors
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```
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We present a new method of succinctly determining eigenvectors
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from eigenvalues. Specifically, we relate the norm squared of the elements of
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eigenvectors to the eigenvalues and the submatrix eigenvalues."
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eigenvectors to the eigenvalues and the submatrix eigenvalues.
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```
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## Core Equation
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![](./images/lemma2.png)
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This is the core equation you will notice being referenced as `equation 2` in the code.
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## Dependencies
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- PyTorch 1.3.1
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- PyTorch 1.3.1 (can be most versions of PyTorch as I used very core basic PyTorch functions)
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- Python 3.6
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## Full Credits
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- [Original authors' paper](https://arxiv.org/pdf/1908.03795.pdf)
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- [Original authors' paper: Eigenvectors from Eigenvalues](https://arxiv.org/pdf/1908.03795.pdf)
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- [Quantamagazine article: Neutrinos Lead to Unexpected Discovery in Basic Math](https://www.quantamagazine.org/neutrinos-lead-to-unexpected-discovery-in-basic-math-20191113/)
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- [Leo Dirac numpy implementation](https://github.com/leopd/geometric-intuition/blob/master/linear-algebra/eigenvectors%20from%20eigenvalues.ipynb)
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Full credits given to the **original authors** and the **numpy implementation by Leo Dirac**.
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## License
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MIT

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