# matrix multiplication

(2.1 hours to learn)

## Summary

Matrix multiplication is an operator on matrices which satisfies many of the properties of multiplication, although not commutativity.

## Context

This concept has the prerequisites:

- dot product (Matrix multiplication is defined in terms of the dot product.)

## Core resources (read/watch one of the following)

## -Free-

→ Khan Academy: Linear Algebra

Other notes:

- Watch the lecture sequence "Functions and linear transformations" if you're not used to thinking of matrices as linear transformations.

→ MIT Open Courseware: Linear Algebra (2011)

Videos for an introductory linear algebra course focusing on numerical methods.

## -Paid-

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 1.4, "Linear transformations and matrix algebra," up to subsection 4.2, "The transpose," pages 23-36

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 2.4, up to "Block matrices and block multiplication," pages 67-70

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ A First Course in Linear Algebra (2012)

A linear algebra textbook with proofs.

## See also

- Common operations on matrices include:
- matrix inverse , which is useful for [solving systems of linear equations](linear_systems_as_matrices)
- eigenvalues , a central concept in many areas of science and engineering
- the singular value decomposition , a canonical representation of matrices closely related to eigenvalues