# Eigenvalues and Eigenvectors

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Lesson Summary:

This lesson covers the concept of eigenvalues and eigenvectors, which are special numbers and vectors found in square matrices. Eigenvectors are vectors that remain in the same direction after being multiplied by a matrix, while eigenvalues are the factors by which the eigenvectors are scaled. The lecture explains how to find eigenvalues and eigenvectors using the characteristic equation and how to determine the number of distinct eigenvalues in a matrix. The lesson also includes examples of projection and permutation matrices to demonstrate the application of eigenvalues and eigenvectors in real-world problems.

Lesson Description:

Eigenvalues and Eigenvectors -- Lecture 21. What are they? What do they mean?

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.