Eigenvalues and Eigenvectors
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.
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.
More info at: http://ocw.mit.edu/terms
- Eigenvector Demo - A Java demo of eigenvectors for 2x2 matrices. Learn what it means to have an eigenvector geometrically.
- Eigenvector Applet - The Java Eigenvector applet for you to play around with that was used and goes along with the demo.
- Eigenvalue / Eigenvector Mini-Lecture - This is a mini-lecture demo lesson on eigenvalues and eigenvectors.
- Eigenvector / determinant Mini-Lecture - This is a mini-lecture demo lesson on finding eigenvalues / eigenvectors and using the determinant of a matrix.
- What is an Eigenvalue?
- What is an Eigenvector?
- How do you find Eigenvalues for a matrix?
- How do you find the Eigenvectors for a matrix?
- What does lambda mean in Linear Algebra?
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Staff Review
An introduction to a vital aspect of Linear Algebra, Eigenvalues and Eigenvectors. This video explains in good detail what it means to have these numbers, what they represent, and how they will be used in the future. A great starting point for understanding these numbers.
