Unit 2 · Vector Spaces and the Four Subspaces

Chapter 2.4

The Four Fundamental Subspaces

Every matrix carries four subspaces — row space, column space, and two nullspaces — with dimensions locked by rank and orthogonality hiding in the pairing. The big picture of the course, on one diagram.

12–16 min · lesson 7 of 21

By the end

  1. 01Identify the four fundamental subspaces of a matrix
  2. 02State and use their dimensions in terms of rank
  3. 03Draw the big picture: how the four subspaces fit together

In unit 2

  1. 2.1Vector Spaces, Subspaces, and the Nullspace12–16
  2. 2.2The Complete Solution to Ax = b12–16
  3. 2.3Independence, Basis, and Dimension11–15
  4. 2.4The Four Fundamental Subspaces12–16
  5. 2.5Graphs and Networks11–15
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