Power Method for Dominant Eigenvalues and Eigenvectors | Linear Algebra

🛍 Check out the coolest math clothes in the world! https://mathshion.com/ Linear Algebra course:    • Linear Algebra   Linear Algebra exercises:    • Linear Algebra Exercises   📚 Get the textbook for this course! https://amzn.to/45KYgmA Business Inquiries: [email protected] Continuing our chapter on numerical analysis, we introduce the power method with maximum entry scaling and with Euclidean scaling for approximating dominant eigenvectors and dominant eigenvalues of symmetric matrices. We'll define power sequences and dominant eigenvalues and dominant eigenvectors. We'll do an example performing six iterations of the power method for approximating dominant eigenvectors and then use the Rayleigh quotient to approximate the corresponding dominant eigenvalue. #linearalgebra ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● TikTok:   / wrathofmathedu   ● X: https://x.com/wrathofmathedu 0:00 Intro 0:18 Definition of Power Sequence and Dominant Eigenvalues/Eigenvectors 1:09 Dominant Eigenvalue Example 1:59 Power Method Approximation 3:31 If the Dominant Eigenvalue is Negative 4:35 Rayleigh Quotient 5:47 Using the Power Method 7:52 Start 9:08 Arriving at Approximation 10:55 Issue of Scale 12:00 Maximum Entry Scaling 14:00 Euclidean Scaling 15:35 Geometric Intuition 19:47 Conclusion