math115: fix eigen def

This commit is contained in:
eggy 2022-12-04 18:24:38 -05:00
parent ae0489b522
commit 4812aafe94

View File

@ -943,8 +943,8 @@ $$(A-\lambda I)\vec x=\vec 0$$
The determinant of the system can be used to check if there will be any eigenvectors.
- If $\det(A-\lambda I)=0$, there is exactly one solution which is the trivial solution, so $\lambda$ is **not an eigenvalue**.
- If $\det(A-\lambda I)\neq 0$, there are multiple solutions, so $\lambda$ is an eigenvalue.
- If $\det(A-\lambda I)=0$, there is exactly one solution which is the trivial solution, so $\lambda$ is **an eigenvalue**.
- If $\det(A-\lambda I)\neq 0$, there are multiple solutions, so $\lambda$ is **not** an eigenvalue.
The **characteristic polynomial** of an eigenvalue is equal to its determinant, and can be used to solve for eigenvalues when $\lambda$ is unknown.