Explore the fundamental concept of eigenvalues and eigenvectors in linear algebra through this 34-minute video lecture. Discover how eigenvectors represent a change of coordinates that diagonalizes a matrix, with eigenvalues as the diagonal entries. Learn to solve complex linear systems of differential equations using these powerful tools. Follow along as the instructor demonstrates the eigenvalue equation, explains why eigenvalues and eigenvectors are special, and works through a 2x2 matrix example. Gain insights into computing eigenvalues and eigenvectors for any matrix, understand how determinants measure the area of a transformation, and see the process applied to both 2x2 and 3x3 matrices. Perfect for students and professionals looking to deepen their understanding of this crucial linear algebra concept.