Skip to content

Instantly share code, notes, and snippets.

@mobeets

mobeets/index.md

Last active August 29, 2015 14:05
Show Gist options
  • Star 0 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save mobeets/4fd6e183767f732f1220 to your computer and use it in GitHub Desktop.
Save mobeets/4fd6e183767f732f1220 to your computer and use it in GitHub Desktop.
Download ZIP
square matrix facts
Raw
index.md

Defintions

For some matrix A:

  • A is symmetric ⇔ A = A'
  • A is positive definite ⇔ for every non-zero vector x, x'Ax > 0
  • A is non-singular ⇔ A is invertible ⇔ detA≠0 ⇔ there exists B such that AB = BA = I
  • A is a distance matrix ⇔ A is symmetric and diag(A) = 0

Fun facts

  1. A is non-singular ⇒ AA' is positive definite
  2. A is symmetric ⇒ AA is positive definite
  3. A is distance matrix ⇒ squared distance matrix AA is positive definite
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment