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Subsection 9.1.3 What you will learn

This week, you are reintroduced to the theory of eigenvalues, eigenvectors, and diagonalization. Building on this, we start our discovery of practical algorithms.

Upon completion of this week, you should be able to

  • Connect the algebraic eigenvalue problem to the various ways in which singular matrices can be characterized.

  • Relate diagonalization of a matrix to the eigenvalue problem.

  • Link the eigenvalue problem to the Schur and Spectral Decompositions of a matrix.

  • Translate theoretical insights into a practical Power Method and related methods.

  • Investigate the convergence properties of practical algorithms.