Explore the fundamental properties of eigenvalues in this concise 12-minute lecture. Delve into the mathematical concepts and characteristics that define eigenvalues, gaining a deeper understanding of their significance in linear algebra. Learn how eigenvalues relate to matrices, their role in solving systems of equations, and their applications in various fields of mathematics and science. Enhance your knowledge of linear transformations and their relationship to eigenvalues, equipping yourself with essential tools for advanced mathematical analysis.