Unit III: Positive Definite Matrices and Applications

Linear Transformations and their Matrices

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Session Overview

Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

When we multiply a matrix by an input vector we get an output vector, often in a new space. We can ask what this “linear transformation” does to all the vectors in a space. In fact, matrices were originally invented for the study of linear transformations.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 7.1 in the 4th edition or Section 8.1 in the 5th edition.

Problem Solving Video

Check Yourself

Problems and Solutions

Work the problems on your own and check your answers when you’re done.

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Course Info

Learning Resource Types

theaters Lecture Videos
grading Exams with Solutions
notes Lecture Notes
theaters Recitation Videos
assignment_turned_in Problem Sets with Solutions
laptop_windows Simulations
groups Course Introduction
co_present Instructor Insights