eigenvector

In mathematics, an eigenvector is a nonzero vector that, when a linear transformation is applied to it, results in a vector that is simply a scalar multiple of the original eigenvector. This scalar is known as the eigenvalue. Essentially, the direction of the eigenvector remains unchanged by the transformation, only its magnitude is scaled.12

Eigenvectors and eigenvalues are fundamental concepts in linear algebra, a field that studies vectors, matrices, and vector spaces. They are particularly useful for understanding the long-term behavior of systems that involve repeated transformations, as arbitrary vectors tend to converge towards the eigenvector associated with the largest eigenvalue. This concept has wide-ranging applications in various scientific and engineering fields.3