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ritchieng committed Nov 18, 2019
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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.

Full credits given to the **original authors** and the **numpy implementation by Leo Dirac**.

I ported this to PyTorch as a lot of my workflows are on the GPUs with PyTorch.

## 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)

## Authors and Abstract
PETER B. DENTON, STEPHEN J. PARKE, TERENCE TAO, AND XINING ZHANG

"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.
```

## Core Equation
![](./images/lemma2.png)

This is the core equation you will notice being referenced as `equation 2` in the code.

## 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

## 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)

Full credits given to the **original authors** and the **numpy implementation by Leo Dirac**.

## License
MIT

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