Eigenvectors and eigenvalues are mathematical concepts that are used to describe the behavior of linear transformations. A linear transformation is a function that takes a vector as input and produces another vector as output. Eigenvectors are vectors that are not changed by the linear transformation, except for a scaling factor. Eigenvalues are the scaling factors that correspond to the eigenvectors.
Eigenvectors and eigenvalues are important because they can be used to understand the behavior of a linear transformation. For example, the eigenvectors of a rotation matrix are the axes of rotation, and the eigenvalues are the angles of rotation. The eigenvectors of a scaling matrix are the directions in which the matrix scales the input vector, and the eigenvalues are the scaling factors.
