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# New Eigenvectors from Eigenvalues Calculation | ||
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 | ||
[![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) | ||
[![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 | ||
PETER B. DENTON, STEPHEN J. PARKE, TERENCE TAO, AND XINING ZHANG | ||
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"We present a new method of succinctly determining eigenvectors | ||
``` | ||
We present a new method of succinctly determining eigenvectors | ||
from eigenvalues. Specifically, we relate the norm squared of the elements of | ||
eigenvectors to the eigenvalues and the submatrix eigenvalues." | ||
eigenvectors to the eigenvalues and the submatrix eigenvalues. | ||
``` | ||
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## Core Equation | ||
![](./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 | ||
- PyTorch 1.3.1 | ||
- PyTorch 1.3.1 (can be most versions of PyTorch as I used very core basic PyTorch functions) | ||
- Python 3.6 | ||
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## Full Credits | ||
- [Original authors' paper](https://arxiv.org/pdf/1908.03795.pdf) | ||
- [Original authors' paper: Eigenvectors from Eigenvalues](https://arxiv.org/pdf/1908.03795.pdf) | ||
- [Quantamagazine article: Neutrinos Lead to Unexpected Discovery in Basic Math](https://www.quantamagazine.org/neutrinos-lead-to-unexpected-discovery-in-basic-math-20191113/) | ||
- [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 | ||
MIT |