Eigenvectors and eigenvalues are mathematical ideas which might be used to explain the habits of linear transformations. A linear transformation is a perform that takes a vector as enter and produces one other vector as output. Eigenvectors are vectors that aren’t modified by the linear transformation, aside from a scaling issue. Eigenvalues are the scaling components that correspond to the eigenvectors.
Eigenvectors and eigenvalues are essential as a result of they can be utilized to grasp the habits of a linear transformation. For instance, 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 instructions by which the matrix scales the enter vector, and the eigenvalues are the scaling components.
