THE PURPOSE OF EIGENVALUE AND EIGENVECTOR

1. In Power Engineering, calculating the Electric & Magnetic fields, corona discharge, and impedance (zero, positive, and negative) of transmission line.2. Natural frequencies and mode shapes in dynamic systems are obtained by solving the Eigen system3. Eigenvalues and eigenvectors can be used in sensitivity equation to find mass and/or stiffness change in structures.4. To find the vibrating in vibrating system example water ripple, road decomposer and so on5. Understanding linear transformations easy. They are the "axes" (directions) along which a linear transformation acts simply by "stretching/compressing" and/or "flipping"; eigenvalues give you the factors by which this compression occurs.6. Most of the dynamic analysis is performed with modal analysis; hence Eigen value problem is widely used for dynamic analysis. Without Eigen value and Eigen vectors dynamic analysis would be so difficult to solve.7. Eigenvalues and eigenvectors find useful applications in stability problems. Stability problems are usually posed in either of the forms 1. [K]-p[Kg]=0 (linear eigenvalue problem) or 2. [K]=0 (non-linear eigenvalue problem). The first form produces finite number of eigenvalues and their corresponding eigenvectors and is amenable to hand calculations for problems involving 2x2 or 3x3 matrix.8. Furthermore of response modal spectral seismic analysis Eigen value and Eigen vector can be used to get the buckling behavior of p delta nonlinear analysis.9. Eigen vectors and Eigen values are the mode shapes which are used to uncouple the dynamic equilibrium equations for mode superposition and/or response spectrum analyses.10. For electrical engineering, eigenvalue or eigenvector analysis has a large role in the simulation of power systems, particularly in the realm of dynamic stability simulations.11. Hydrogen atom with Coulomb interaction between the electron and the nucleus and apply Schrdinger's equation; the energy's of the allowed orbits are the eigenvalues of this differential equation, and the eigenvectors are the allowed orbitals. In this manner eigenvalues are fundamental to our understanding of basic matter.