The interactive film is in the book's Companion

Play it, pause it, turn it and drag it with Mathematics for AI and Machine Learning.

Get the book

Numerical Rank: When Is a Pancake a Plane?

Chapter 4 · Mathematics for AI and Machine Learning · Advanced · 1:24

An interactive live film: a thin 3 x 40 point cloud and its singular axes; the numerical rank counts singular values above epsilon times the largest. Choose epsilon so the pancake counts as a plane.

Narration

Here are forty columns of a matrix with three rows, drawn as points. They lie almost in a plane, but noise gives the cloud a little thickness.

The exact rank is three: no column is exactly a combination of the others. But that answer is about the noise, not the data.

The rest of the narration is in the book's Companion.

More from Chapter 4

Interactive1:51Householder Reflection: A Mirror That Clears a ColumnChapter 4Preview1:30The Rank of a Product: Dimensions Can Only Be LostChapter 4Preview1:56Householder QR: One Mirror per ColumnChapter 4Preview1:39Gram-Schmidt or Householder: Losing the Right AnglesChapter 4Preview1:41A Rank-One Change of the Identity: Identity, Projection, MirrorChapter 4