Unit 3 · Orthogonality and Least Squares

Chapter 3.1

Orthogonality and Projections

Perpendicularity does the heavy lifting: the row space meets the nullspace at a right angle, and projecting onto a subspace is a formula, not a picture.

12–16 min · in preparation · lesson 9 of 21

By the end

  1. 01Verify orthogonality of vectors and of the fundamental subspaces
  2. 02Project a vector onto a line and onto a subspace
  3. 03Build projection matrices and state their properties

In unit 3

  1. 3.1Orthogonality and Projections12–16
  2. 3.2Least Squares12–16
  3. 3.3Gram-Schmidt and A = QR11–15
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