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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

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