About This Chapter
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|
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.
Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.