Eigenvalues are special numbers associated with a square matrix in linear algebra. When a matrix acts on a vector, it usually changes both the direction and the length of that vector. However, for certain vectors, known as eigenvectors, the direction remains unchanged, and the only change is in their length. The eigenvalue is the factor by which the eigenvector is stretched or compressed during this transformation. In practical terms, eigenvalues help us understand systems in various fields, such as physics, engineering, and data science. For example, in machine learning, they are used in techniques like Principal Component Analysis (PCA) to reduce the dimensionality of data while preserving its essential features.