This depicts the result of one iteration of the algorithm in the form of a GIF animation. The ellipses denote positive-definite symmetric matrices. Su

ogogmad / la-vis

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2021-08-09 08:30:42

This depicts the result of one iteration of the algorithm in the form of a GIF animation. The ellipses denote positive-definite symmetric matrices. Such a representation by ellipses is possible because of the spectral theorem. Notice how the output is a continuous function of the input. Also notice how as the input matrix is rotated, it encounters two fixed points corresponding to its diagonalisations. One of these fixed points is stable, while the other is unstable.

The link to the Python code is here. It uses Pygame and Numpy, and is very, very rough (as a minimum viable product should be). It would be better if it could run in a browser.

Many algorithms (like the QR algorithm for finding eigenvalues) are described in ways that are hard to understand. Specifically, it's unclear why these algorithms achieve their objectives. This is especially mysterious when the algorithms are based on fixed-point iteration, like the QR algorithm. In this repository, we hope to introduce interactive visualisations of linear algebra algorithms which should enable someone to understand how a given algorithm behaves when its inputs are varied.

The visualisations should be interactive wherever possible. The reason for this is that it allows someone to see how the output of an algorithm varies when its input is changed. This can enable someone to see how the input influences convergence rate.

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