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- Study the definition and equations of eigenvalue and eigenvector.
- Review how to determine the eigenvalues and eigenvectors of a matrix.
- Understand how to define eigenspaces.
- Examine diagonalization.
- Describe 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.
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