Unit 2 · Vector Spaces and the Four Subspaces

Chapter 2.5

Graphs and Networks

A graph becomes a matrix, and the four subspaces become physics: Kirchhoff's laws are statements about nullspaces.

11–15 min · lesson 8 of 21

By the end

  1. 01Build the incidence matrix of a graph
  2. 02Interpret its subspaces as potentials, loops, and conservation laws
  3. 03Connect rank to the structure of the network

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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