Eigenvectors are a mathematical concept that are used in a wide range of fields including mathematics, physics, engineering, and computer science. An eigenvector of a linear transformation is a non-zero vector that only changes in scale when that transformation is applied. In other words, the eigenvector remains in the same direction but may grow or shrink in length. Eigenvectors are important in the study of linear algebra as they provide insights into the properties of matrices and their transformations. They are used in applications such as finding the principal components of data, solving systems of differential equations, and analyzing the stability of dynamic systems. Overall, eigenvectors are a fundamental concept in linear algebra and are widely used in various scientific and engineering disciplines.