About This Chapter
Who's It For?
Anyone who needs help learning or mastering eigenvalues and eigenvectors material will benefit from the lessons in this chapter. There is no faster or easier way to learn eigenvalues and eigenvectors. Among those who would benefit are:
- Students who have fallen behind in understanding working with eigenvalues and eigenvectors
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about eigenvalues and eigenvectors
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How It Works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the eigenvalue and eigenvector chapter exam.
Why It Works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the complex numbers chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any question related to eigenvalues and eigenvectors. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students Will Review:
This chapter helps students review the concepts in a eigenvalue and eigenvector unit of a standard linear algebra course. Topics covered include:
- The definition of eigenvalues and eigenvectors
- Finding the eigenvalues of a matrix
- Methods for finding the eigvenvectors of a matrix
- Calculating the eigenspace
- The definition of diagonalization
1. Eigenvalues & Eigenvectors: Definition, Equation & Examples
Every square matrix has special values called eigenvalues. These special eigenvalues and their corresponding eigenvectors are frequently used when applying linear algebra to other areas of mathematics.
2. How to Determine the Eigenvalues of a Matrix
Together we'll learn how to find the eigenvalues of any square matrix. Once we've got that down we'll practice finding eigenvalues by going through an example with a 2x2 matrix, and one with a 3x3 matrix.
3. How to Determine the Eigenvectors of a Matrix
In this lesson, you'll explore the subject of eigenvectors. After learning what an eigenvector is in concept, we'll solidify in your mind how to find them by working through an example problem together.
4. Diagonalization: Definition & Example
Diagonalization is the process of transforming a matrix into diagonal form. Diagonal matrices represent the eigenvalues of a matrix in a clear manner. This lesson will focus on finding the diagonalized form of a simple matrix.
5. Diagonalizing Symmetric Matrices: Definition & Examples
In this lesson, we define symmetric and diagonal matrices. We then use eigenvalues and eigenvectors to form a very special matrix which is then used to diagonalize a symmetric matrix.
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