❖ Introduction to Eigenvalues and Eigenvectors - Part 1 ❖

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 Support My Channel on Patreon: https://www.patreon.com/patrickjmt?ty=c 👍 Don’t forget to like, subscribe, and hit the notification bell for more math tutorials and problem-solving tips! 🔔✨ #Eigenvalues #Eigenvectors #LinearAlgebra #MatrixAlgebra #MathTutorial #LearningMath #STEM #Mathematics #MathHelp #LinearEquations #MathProblems