matrix inverse
(1.8 hours to learn)
Summary
The inverse of a matrix A is a matrix which, when multiplied by A, gives the identity matrix. When it exists, it can be used to solve systems of linear equations.
Context
This concept has the prerequisites:
- linear systems as matrices (The matrix inverse is defined in terms of systems of linear equations.)
- matrix multiplication (The inverse of a product is the product of the inverses, reversed.)
Core resources (read/watch one of the following)
-Free-
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
→ Khan Academy: Linear Algebra
Other notes:
- Watch the "Functions and linear transformations" lecture sequence if you're not used to thinking of matrices as linear transformations.
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.
-Paid-
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location:
Section 2.5, up to "Calculating A^-1 by Gauss-Jordan elimination", pages 81-83
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location:
Section 1.4.1, "Algebra of linear functions," from pages 34-36
See also
- The inverse of a matrix can be interpreted in terms of systems of linear equations .