Linear Algebra › Section B · Matrix algebra › Topic B.1

Matrix operations

A matrix is more than a table of numbers: it can be added, scaled, multiplied and flipped. Matrix multiplication in particular is defined so that it chains transformations together, and that one decision explains every rule in this topic.

In this topic

  • From tables to an algebra
  • Notation and special matrices
  • Sums and scalar multiples
  • Multiplication means composition
  • The row-column rule
  • Worked example: a 2 × 3 times a 3 × 2
  • Properties, and what fails
  • Worked example: revenue and cost for three shops
  • Powers and the transpose
  • Common mistakes to avoid
  • Key takeaways

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