All of my resources for numerical analysis show that the spectral
decomposition is
A = CBC'
Where C are the eigenvectors and B is a diagonal matrix of eigen values.
Now, using the eigen function in R
# Original matrix
aa - matrix(c(1,-1,-1,1), ncol=2)
ss - eigen(aa)
# This results yields back
For a general square matrix A, the eigenvalue decomposition is
A = CBC^{-1}
For the special case of symmetric A,
C^{-1} = C'
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On 29-Jun-07 13:23:05, Ted Harding wrote:
[Sorry -- a silly typo in my previous]:
If A is not symmetric, you have left eigenvectors:
x'*A = lambda*x'
and right eigenvectors:
A*x = lambda*x
and the left eigenvectors are not the same as the right
eigenvectors, though you have the
On 29-Jun-07 12:29:31, Doran, Harold wrote:
All of my resources for numerical analysis show that the spectral
decomposition is
A = CBC'
Where C are the eigenvectors and B is a diagonal matrix of eigen
values. Now, using the eigen function in R
# Original matrix
aa -
