Get the eigenbasis associated with an eigenvalue based on the representation
of a Hermitian Matrix given by class spectral.
Usage
# S3 method for spectral
get_eigspace(object, id, ...)Arguments
- object
an instance of class
spectral.- id
index for the desired eigenspace according to the ordered (decreasing) spectra.
- ...
further arguments passed to or from other methods.
Value
A matrix whose columns form the orthonormal eigenbasis.
If s <- spectral(A) and V <- s$eigvectors, then the extracted eigenspace
\(V_{id}\) is some submatrix V[, _].
Examples
# Spectra is {2, -1} with multiplicities one and two respectively.
decomp <- spectral(matrix(c(0,1,1,1,0,1,1,1,0), nrow=3))
# Returns the two orthonormal eigenvectors corresponding to the eigenvalue -1.
get_eigspace(decomp, id=2)
#> [,1] [,2]
#> [1,] 0.8164966 0.0000000
#> [2,] -0.4082483 -0.7071068
#> [3,] -0.4082483 0.7071068
# Returns the eigenvector corresponding to the eigenvalue 2.
get_eigspace(decomp, id=1)
#> [,1]
#> [1,] 0.5773503
#> [2,] 0.5773503
#> [3,] 0.5773503