Some applications of matrixes'es eigenvalues and matrixes'es eigenvectors

Eigenvalue and eigenvector problems arise in many engineering applications. In this thesis, we consider some matrices which are important ones in applications. The elements of these matrices consist of cartesian components of the mass and area inertia tensors, stress tensor and strain tensor. We give the physical meanings and some facilities of eigenvalues and eigenvectors of these matrices. Moreover we obtained the transformation equations of the mentioned matrices and we showed that they are actually the tensor transformation relations. Key words: Symmetric matrixes, eigenvalue, eigenvector, quadratic form, moment of inertia, flexure, stress, deformation.