From 87109cc1a30e779967725e9e5494b526c256b67a Mon Sep 17 00:00:00 2001 From: Ritchie Ng Date: Mon, 18 Nov 2019 08:55:36 +0800 Subject: [PATCH] Update Docs --- README.md | 17 ++++++++++------- 1 file changed, 10 insertions(+), 7 deletions(-) diff --git a/README.md b/README.md index f198a20..05a3574 100644 --- a/README.md +++ b/README.md @@ -1,19 +1,19 @@ # 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) @@ -21,12 +21,15 @@ eigenvectors to the eigenvalues and the submatrix eigenvalues." 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