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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