Left and Right Inverses; Pseudoinverse

OCW Scholar

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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 textbook.

Problem Solving Video

  • Watch the recitation video on Pseudoinverses (00:14:39)
  • Recitation video transcript (PDF)

Check Yourself

Problems and Solutions

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


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