WuTheFWasThat / EigenSeeClearlyNow

Linear algebra visualizations

EIGEN SEE CLEARLY NOW

OVERVIEW

This is a project to help anyone learning linear algebra visualize its concepts.

It is still an early-stage work in progress.

Click here for a partial demo.

SETUP

Install:

git clone https://github.com/WuTheFWasThat/EigenSeeClearlyNow.git
cd EigenSeeClearlyNow
npm install

Start:

npm start

Then just hit port 8080 on localhost

TO-DO:

• matrix * vector

• matrix * matrix

• matrices!

• make gridding better?

• make distances/etc aspects of view configurable?

• make keyboard handler more flexible?

• make prod version work: NODE_ENV=production ./node_modules/.bin/coffee server.coffee

IDEAS:

• determinant
• independence (as a game?)
• make span game 2! (hint: Try rotating the camera so that one basis vector lines up with the origin. You should be able to visually prove that this game is impossible!)
  • refactor span game!
• symmetric matrix
• orthogonal matrix
• inverse
• eigenvalue
• something where you find eigenvalue by sliding around lambda in (A - lambda I)?
• SVD

TOPICS:

• subspace
• Nullspace
• Colspace
• span
• independence
• bases Square matrices:
  1. matrix is invertible if 1 to 1 inverse matrix
  2. change of basis Symmetric matrices:
  3. two vectors are orthogonal if dot product is zero. to see this, change bases
  4. orthogonal projection
  5. have orthonormal set of eigenvalues

more: eigenvectors spectral theora

advanced: dual space? direct sum?

KNOWN ISSUES:

CONTRIBUTE:

Feel free to send me pull requests!

For the visualizations, we use three.js. Many thanks to them!

CONTRIBUTORS:

• Jeff Wu
• Yang Hong