The interactive film is in the book's Companion

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Rank-Revealing QR: Pick the Columns in a Good Order

Chapter 9 · Mathematics for AI and Machine Learning · Advanced · 1:47

An interactive live film: QR with column pivoting on the book's rank-two example in 3D; the longest column first, the leftovers in the plane perpendicular to q0, and a last diagonal entry that reveals the rank; the reader pushes a column out of the plane and sets the tolerance.

Narration

This matrix has three columns in three dimensions, but the third is the sum of the first two, so its rank is two. Rank revealing QR finds that out by taking the columns in a good order.

Start with the longest column, a two, of length seven. It becomes the first direction, q zero.

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

More from Chapter 9

Interactive1:34LoRA: a Low-Rank UpdateChapter 9Preview1:48LDL Is Completing the SquareChapter 9Preview1:25Superposition and Sparse CodingChapter 9Preview1:56The QR Algorithm: Sweeping a Matrix into Schur FormChapter 9Preview1:36Non-Negative Matrix Factorization: a Cone of PartsChapter 9Preview1:33CUR: Rebuilding a Matrix from Its Own Rows and ColumnsChapter 9