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Ch 6: Eigenvalue and Eigenvector in Linear Algebra Lesson Plans

About This Chapter

The Eigenvalue and Eigenvector in Linear Algebra chapter of this course is designed to help you plan and teach the definitions and equations associated with eigenvalue, eigenvector and matrices in your classroom. The video lessons, quizzes and transcripts can easily be adapted to provide your lesson plans with engaging and dynamic educational content. Make planning your course easier by using our syllabus as a guide.

Weekly Syllabus

Below is a sample breakdown of the Eigenvalue and Eigenvector in Linear Algebra chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day Topics Key Terms and Concepts Covered
Monday Eigenvalue and eigenvector overview Definitions of eigenvalue and eigenvector, linear operator, vector, nonzero vector, scalar, matrix
Tuesday Eigenvalues and eigenvectors of a matrix Square matrices, monic polynomial, characteristic polynomial, characteristic equation, Laplace expansion, Cayley-Hamilton Theorem
Wednesday Eigenspaces Eigenspaces, scalar multiplication, vector addition, zero vector, nullspace
Thursday Diagonalization Used of diagonalization, diagonal matrix, linearly independent eigenvectors
Friday Diagonalization of symmetric matrices Definition and 3x3 example of diagonalizing symmetric matrices

5 Lessons in Chapter 6: Eigenvalue and Eigenvector in Linear Algebra Lesson Plans
Test your knowledge with a 30-question chapter practice test
Eigenvalues & Eigenvectors: Definition, Equation & Examples

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.

How to Determine the Eigenvalues of a Matrix

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.

How to Determine the Eigenvectors of a 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.

Diagonalization: Definition & Example

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.

Diagonalizing Symmetric Matrices: Definition & Examples

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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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