Eigenvectors are special vectors in linear algebra that, when transformed by a matrix, only change in scale and not in direction. This means that if you apply a matrix to an eigenvector, the result is a new vector that points in the same direction as the original, but may be longer or shorter. Each eigenvector is associated with a specific value called an eigenvalue, which indicates how much the eigenvector is stretched or compressed during the transformation. Eigenvectors and eigenvalues are important in various fields, including physics, engineering, and data science, as they help simplify complex problems.