An eigenvector is a special type of vector in linear algebra that, when transformed by a given linear transformation, changes only in scale and not in direction. This means that if you apply a matrix to an eigenvector, the result is simply a scaled version of that eigenvector. The scaling factor is known as the eigenvalue. Eigenvectors are important in various fields, including physics, computer science, and statistics. They help in simplifying complex problems, such as those found in machine learning and quantum mechanics, by allowing us to analyze systems in terms of their fundamental directions and behaviors.