get_eigschur.spectral: Extract a Schur Cross-Product from a Hermitian Matrix

In qwalkr: Handle Continuous-Time Quantum Walks with R

Extract a Schur Cross-Product from a Hermitian Matrix

Description

Get the Schur product between eigen-projectors based on the representation of a Hermitian Matrix given by class spectral.

Usage

## S3 method for class 'spectral'
get_eigschur(object, id1, id2 = NULL, ...)

Arguments

object	an instance of class spectral.
id1	index for the first eigenspace according to the ordered (decreasing) spectra.
id2	index for the second eigenspace according to the ordered (decreasing) spectra. If not provided, it takes the same value as id1.
...	further arguments passed to or from other methods.

Value

The Schur product of the corresponding eigenprojectors, E_{id_1} \circ E_{id_2}.

See Also

spectral(), get_eigschur()

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 Schur product between the 2-projector and -1-projector.
get_eigschur(decomp, id1=2, id2=1)

# Returns the Schur square of the 2-projector.
get_eigschur(decomp, id1=1, id2=1)

# Also returns the Schur square of the 2-projector
get_eigschur(decomp, id1=1)

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