Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Matrix Diagonalization & Eigen Decomposition

  1. Nov 11, 2013 #1
    Do these terms practically refer to the same thing?
    Like a matrix is diagonalizable iff it can be expressed in the form A=PDP[itex]^{-1}[/itex], where A is n×n matrix, P is an invertible n×n matrix, and D is a diagonal matrix
    Now, this relationship between the eigenvalues/eigenvectors is sometimes referred to as eigen decomposition? Can someone clarify these terms for me.
  2. jcsd
  3. Nov 19, 2013 #2
    I think eigen decomposition is another term for spectral decomposition in the spectral theorem. Although it is stated in a different way than diagonalizing a matrix, the spectral decomposition is related to the Schur decomposition for normal linear transformations.
  4. Nov 19, 2013 #3


    User Avatar
    Science Advisor
    Homework Helper

    For a matrix they are basically the same, but the concept of eigenvalues/vectors applies to other situations as well. For example the solution of ODEs and PDEs can involve infinite-dimensional vector spaces (and even uncountably infinite dimensional spaces), where "matrices" are not a very useful tool to work with.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook