Eigenvectors and eigenvalues are mathematical ideas which might be used to explain the conduct of linear transformations. A linear transformation is a operate that takes a vector as enter and produces one other vector as output. Eigenvectors are vectors that aren’t modified by the linear transformation, apart from a scaling issue. Eigenvalues are the scaling components that correspond to the eigenvectors.
Eigenvectors and eigenvalues are necessary as a result of they can be utilized to grasp the conduct 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.
