Oxford Linear Algebra - Eigenvalues and Eigenvectors Explained

Explore the fundamental concepts of eigenvalues and eigenvectors in this 26-minute video lecture by University of Oxford mathematician Dr. Tom Crawford. Learn how to calculate eigenvalues and eigenvectors of matrices through two fully worked examples. Begin with an introduction to the eigenvalue equation and discuss possible solution methods. Understand why a non-zero eigenvector can only be found when the determinant of the characteristic matrix is zero, leading to the characteristic equation or polynomial. Follow along as Dr. Crawford demonstrates the method using both 2x2 and 3x3 matrix examples, considering general eigenvectors before simplifying the final vector. Access additional practice exercises, video lectures, and worked solutions through provided links to enhance your understanding of this crucial linear algebra topic.