ABSTRACT
This chapter introduces the mathematical concepts of eigenvalues and eigenvectors and discusses their usage in engineering related applications. Eigenvalues and eigenvectors have many applications in several engineering disciplines ranging from the analysis of structures in civil engineering to circuit analysis, signal and image processing, and control in electrical engineering. Eigenvalues and eigenvectors have several useful properties. The first property is related to the independence of eigenvectors. The product and sum of the eigenvalues of any matrix are equal to the determinant and trace of that matrix, respectively. An important property of unitary matrices is that the inverse of the matrix is equal to its conjugate transpose. Hermitian matrices play an important role in communication, signal processing and control. The chapter provides a definition for Hermitian matrices and describes their important properties. Positive and negative definite matrices are an important class of matrices with applications in different engineering fields.
