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By Kardi Teknomo, PhD.
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Diagonalization of a real symmetric matrix is also called spectral decomposition, or Schur Decomposition. Given a square symmetric matrix , the matrix can be factorized into two matrices and . Matrix  is an orthogonal matrix . Matrix is a diagonal matrix. Spectral decomposition is matrix factorization because we can multiply the matrices to get back the original matrix .
The interactive program below yield three matrices , and matrix  and also gives you feedback on . Random example will generate random symmetric matrix.
See also: Matrix Eigen Value & Eigen Vector for Symmetric Matrix, Similarity and Matrix Diagonalization, Symmetric Matrix, Singular Value Decomposition
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Preferable reference for this tutorial is
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\
tutorial\LinearAlgebra\ |
