(1.8 hours to learn)
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.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
→ Khan Academy: Linear Algebra
- 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)
→ A First Course in Linear Algebra (2012)
A linear algebra textbook with proofs.
→ 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
- The inverse of a matrix can be interpreted in terms of systems of linear equations .
- create concept: shift + click on graph
- change concept title: shift + click on existing concept
- link together concepts: shift + click drag from one concept to another
- remove concept from graph: click on concept then press delete/backspace
- add associated content to concept: click the small circle that appears on the node when hovering over it
- other actions: use the icons in the upper right corner to optimize the graph placement, preview the graph, or download a json representation