18.06SC | Fall 2011 | Undergraduate

Linear Algebra

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

As Taught In
Fall 2011
Learning Resource Types
Lecture Videos
Exams with Solutions
Lecture Notes
Recitation Videos
Problem Sets with Solutions
Course Introduction
Instructor Insights