👉 Eigenvalues and eigenvectors are fundamental concepts in linear algebra, a branch of mathematics crucial for understanding the behavior of linear transformations. Eigenvalues represent how much a linear transformation stretches or shrinks vectors in specific directions, known as eigenvectors. These eigenvectors are special because they remain in the same direction after transformation, only their magnitude changes by the factor of the eigenvalue. This concept is pivotal in various fields, including physics, engineering, and data science, for tasks like stability analysis, principal component analysis, and solving differential equations. Essentially, eigenvalues and eigenvectors help us understand the intrinsic properties of linear transformations, simplifying complex problems by breaking them down into manageable components.
