Introduction to Eigenvalues and Eigenvectors – Part 1: Definition and Quick Example
In this video, I introduce the concept of eigenvalues and eigenvectors, explaining their definitions clearly. We walk through a specific example showing that a given vector is indeed an eigenvector of a matrix 𝐴 corresponding to the eigenvalue 𝜆 = 4.
Finally, I provide a quick proof demonstrating that if a vector is an eigenvector, then any multiple of that vector is also an eigenvector.
What’s covered:
Definition of eigenvalues and eigenvectors.
Example: Proving a given vector is an eigenvector for matrix 𝐴 with eigenvalue 𝜆 = 4.
Proof: Showing that any scalar multiple of an eigenvector is also an eigenvector.
This is Part 1 of a series on eigenvalues and eigenvectors, perfect for students learning linear algebra or preparing for exams. Make sure to watch Part 2 for a deeper dive into finding eigenvalues and eigenvectors step-by-step.
🔗 Watch Part 2 – Finding Eigenvalues and Eigenvectors:
https://www.youtube.com/watch?v=IdsV0RaC9jM<br />
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