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