While teaching engineering students, many of you face this question "In engineering point of view what is the meaning of eigenvalues and eigenvectors ?"
One of the most efficient transformation in signal processing is called Karhunen-Loeve Transform (KLT),(also known as Hotelling Transform Eigenvector Transform). Where, they consider eigenvalues as coefficients and eigenvectors as basis functions. However, these basis functions are extracted from the data matrix itself.