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 eigenvalue, which indicates how much the eigenvector is stretched or compressed during the transformation. In practical terms, eigenvectors are useful in various fields, including physics, computer science, and data analysis. They help simplify complex problems by breaking them down into more manageable components. For example, in principal component analysis, eigenvectors are used to identify the most important features in a dataset, allowing for more efficient data processing and visualization.