get_eigspace.spectral: Extract an Eigenspace from a Hermitian Matrix

In qwalkr: Handle Continuous-Time Quantum Walks with R

Extract an Eigenspace from a Hermitian Matrix

Description

Get the eigenbasis associated with an eigenvalue based on the representation of a Hermitian Matrix given by class spectral.

Usage

## S3 method for class '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[, _]⁠.

See Also

spectral(), get_eigspace()

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)

# Returns the eigenvector corresponding to the eigenvalue 2.
get_eigspace(decomp, id=1)

qwalkr documentation built on Sept. 27, 2023, 9:09 a.m.