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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

    AlephZero

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    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.
     
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