Linear Transformations and Their Matrices
This lesson on linear transformations and their matrices explores the idea of a linear transformation and how it can make sense without a matrix. However, for most people, coordinates are necessary in order to compute anything, leading to a matrix. The lecture provides examples of linear transformations, including a projection and rotation, and explains the rules for a linear transformation to be considered linear. The goal is to understand linear transformations and find the matrix behind them, which requires bringing in coordinates and choosing a basis.
Linear Transformations and Their Matrices -- Lecture 30. The overarching idea of linear transformations.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
- What is a linear transformation?
- What is a projection?
- What is a mapping?
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Staff Review
An explanation of a very fundamental Linear Algebra topic, linear transformations. This video explains the idea of linear transformations in the way that most courses introduce the course, without matrices or coordinates. Then, transformations are discussed using all of the ideas that have been presented in this course. A truly vital idea in the course.
