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What eigenvalues and eigenvectors mean geometrically

We introduce the idea of eigenvalues and eigenvectors geometrically. Eigenvectors coorespond to a direction where the matrix acts only by stretching, with stretching factor the eigenvalues. This makes the matrix transformation very simple in these directions! How to COMPUTE eigenvalues/eigenvectors:    • Using determinants to compute eigenva...   How to VISUALIZE a basis of eigenvectors:    • Visualizing Diagonalization & Eigenbases   Course Playlists: ►Linear Algebra:    • Linear Algebra (Full Course)   ►Calculus I:    • Calculus I (Limits, Derivative, Integ...   ►Calculus II:    • Older Calculus II (New Playlist For S...   ►Discrete Math:    • Discrete Math (Full Course: Sets, Log...   ***************************************************** ►Follow me on Twitter:   / treforbazett   ***************************************************** This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati. BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett