Eigenvectors and Eigenvalues of a Matrix | Linear Algebra скачать в хорошем качестве

Eigenvectors and Eigenvalues of a Matrix | Linear Algebra

Support the production of this course by joining Wrath of Math to access all my Linear Algebra videos plus lecture notes at the premium tier!    / @wrathofmath   🛍 Check out my math fashion brand! 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: wrathofmathlessons@gmail.com A thorough intro to eigenvectors, eigenvalues, and the characteristic equation and characteristic polynomial of a matrix. We define these terms and do many examples, including eigenvalues and eigenvectors of a 3x3 matrix in addition to several 2x2 examples. We'll go over how to find the eigenvalues of a matrix and how to use those to find the eigenvectors of a matrix. We'll finish with a complex eigenvalue example. #linearalgebra ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Twitter:   / wrathofmathedu   0:00 Intro 0:24 Definition of Eigenvalue and Eigenvector 2:01 Eigenvectors are Nonzero 2:26 Geometric View of Eigenvalues 4:03 How to Verify x is an Eigenvector 5:38 Deriving the Characteristic Equation 8:27 Example of Characteristic Equation 9:10 Use Characteristic Equation to Find Eigenvalues 11:01 Characteristic Polynomial 12:20 Find Eigenvalues of a 3x3 Matrix 13:34 Eigenvectors of a 3x3 Matrix 16:24 Equivalent Eigenvalue Statements 17:25 Complex Eigenvalues 19:34 Conclusion