Question

Importance of eigenvalues and eigenvectors of a matrix

Answer 1

An eigenvector of a matrix is a directions unchanged by the linear transformation: A v = λ v . An eigenvalue of a matrix is unchanged by a change of coordinates: λ v = A v ⇒ λ ( B u ) = A ( B u ) . These are important invariants of linear transformations. Lets Go Back to the Historical Background to get the motivation!