(2.1 hours to learn)
Matrix multiplication is an operator on matrices which satisfies many of the properties of multiplication, although not commutativity.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ Khan Academy: Linear Algebra
- 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.
→ 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)
- 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
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