## Spectral Decomposition

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.

Yes, this program is a free educational program!! Please don't forget to tell your friends and teacher about this awesome program!

**
See also
**
:
Matrix Eigen Value & Eigen Vector for Symmetric Matrix
,
Similarity and Matrix Diagonalization
,
Symmetric Matrix
,
Singular Value Decomposition

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