Eigenvectors and Eigenvalues are mainly used to capture key information that is stored in a large matrix.

  • It provides summary of a large matrix.
  • We can represent large set of information in a matrix and performing computation on a large matrix is slow and requires more memory and CPU. Eigenvectors and Eigenvalues can improve the efficiency in computationally intensive tasks by reducing dimensions after ensuring most of the key information is maintained.
  • Principal component analysis(PCA) is one of the key method which is utilised to reduce dimension space without losing valuable information. The core part of PCA is based on the concept of computing eigenvectors and eigenvalues of the covariance matrix of the features.
  • They are used in facial recognition technique such as Eigenfaces.
  • They are also used to compress data and reduce noise in data.
  • It is used to rank items(page ranking) in a dataset which is widely used in search engines and calculus
  • It is used in image — image matching , 3D reconstruction and linear differential equations.
  • Eigenvalues are used in communication systems to determine the theoretical limit to how much information can be transmitted through a communication medium like your telephone line or through the air. This is done by calculating the eigenvectors and eigenvalues of the communication channel (expressed a matrix), and then waterfilling on the eigenvalues.
  • In Electrical engineering it is useful for decoupling three-phase systems through symmetrical component transformation.
  • In designing bridges, natural frequency of the bridge is the eigenvalue of smallest magnitude of a system that models the bridge. The engineers exploit this knowledge to ensure the stability of their constructions.
  • Oil companies frequently use eigenvalue analysis to explore land for oil. Oil, dirt, and other substances all give rise to linear systems which have different eigenvalues, so eigenvalue analysis can give a good indication of where oil reserves are located. Oil companies place probes around a site to pick up the waves that result from a huge truck used to vibrate the ground. The waves are changed as they pass through the different substances in the ground. The analysis of these waves directs the oil companies to possible drilling sites.