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1 | 1 | # New Eigenvectors from Eigenvalues Calculation
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2 | 2 | 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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3 | 3 |
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4 |
| -Full credits given to the **original authors** and the **numpy implementation by Leo Dirac**. |
5 |
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6 | 4 | I ported this to PyTorch as a lot of my workflows are on the GPUs with PyTorch.
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7 | 5 |
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8 | 6 | ## Run Notebook on Google Colab
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9 |
| -[](https://colab.research.google.com/github/ritchieng/eigenvectors-from-eigenvectors/blob/master/notebooks/comparison.ipynb) |
| 7 | +[](https://colab.research.google.com/github/ritchieng/eigenvectors-from-eigenvalues/blob/master/notebooks/comparison.ipynb) |
10 | 8 |
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11 | 9 | ## Authors and Abstract
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12 | 10 | PETER B. DENTON, STEPHEN J. PARKE, TERENCE TAO, AND XINING ZHANG
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13 | 11 |
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14 |
| -"We present a new method of succinctly determining eigenvectors |
| 12 | +``` |
| 13 | +We present a new method of succinctly determining eigenvectors |
15 | 14 | from eigenvalues. Specifically, we relate the norm squared of the elements of
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16 |
| -eigenvectors to the eigenvalues and the submatrix eigenvalues." |
| 15 | +eigenvectors to the eigenvalues and the submatrix eigenvalues. |
| 16 | +``` |
17 | 17 |
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18 | 18 | ## Core Equation
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19 | 19 | 
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20 | 20 |
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21 | 21 | This is the core equation you will notice being referenced as `equation 2` in the code.
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22 | 22 |
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23 | 23 | ## Dependencies
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24 |
| -- PyTorch 1.3.1 |
| 24 | +- PyTorch 1.3.1 (can be most versions of PyTorch as I used very core basic PyTorch functions) |
25 | 25 | - Python 3.6
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26 | 26 |
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27 | 27 | ## Full Credits
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28 |
| -- [Original authors' paper](https://arxiv.org/pdf/1908.03795.pdf) |
| 28 | +- [Original authors' paper: Eigenvectors from Eigenvalues](https://arxiv.org/pdf/1908.03795.pdf) |
| 29 | +- [Quantamagazine article: Neutrinos Lead to Unexpected Discovery in Basic Math](https://www.quantamagazine.org/neutrinos-lead-to-unexpected-discovery-in-basic-math-20191113/) |
29 | 30 | - [Leo Dirac numpy implementation](https://github.com/leopd/geometric-intuition/blob/master/linear-algebra/eigenvectors%20from%20eigenvalues.ipynb)
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30 | 31 |
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| 32 | +Full credits given to the **original authors** and the **numpy implementation by Leo Dirac**. |
| 33 | + |
31 | 34 | ## License
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32 | 35 | MIT
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