Hi, I have a question for my simulation problem:
I would like to generate a positive (or semi def positive) covariance
matrix, non singular, in wich the spectral decomposition returns me the same
values for all dimensions but differs only in eigenvectors.
Ex.
sigma
[,1] [,2]
[1,] 5.05 4.95
[2,] 4.95 5.05
> eigen(sigma)
$values
[1] 10.0 0.1
$vectors
[,1] [,2]
[1,] 0.7071068 -0.7071068
[2,] 0.7071068 0.7071068
(In theory: Using the spectral decomposition, the matrix Σ can be re-written
as
Σ = 5 ( 1, 1) 1 + 0.05 (1, -1) 1
1 -1 )
This because I would generate another covariance matrix in wich variables
are more than 2.
Thank you
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