Unit III: Positive Definite Matrices and Applications

Left and Right Inverses; Pseudoinverse

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Session Overview

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

We’d like to be able to “invert A” to solve Ax = b, but A may have only a left inverse or right inverse (or no inverse). This discussion of how and when matrices have inverses improves our understanding of the four fundamental subspaces and of many other key topics in the course.

Note: In the Fall of 1999, when the lecture videos were recorded, this lecture was given after exam 3. For the OCW Scholar version of the course we have moved it into the main body of material.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 7.3 in the 4th edition or Section 8.3 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