linear transformations as matrices

(3.4 hours to learn)

Summary

Linear transformations from one vector space to another can be represented as matrices if a basis is given for each space. Common examples include projections, reflections, rotations, and scaling. Linear combinations, compositions and inverses of transformations can be analyzed in terms of matrix operations.

Context

This concept has the prerequisites:

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.
Author: Gilbert Strang
Additional dependencies:
  • bases
  • vector spaces

-Paid-

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.
Author: Robert A. Beezer
Additional dependencies:
  • complex vectors and matrices
  • bases
  • vector spaces

-Paid-

See also

-No Additional Notes-