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Extract a Schur Cross-Product from a Hermitian Matrix

Source: R/linalg.R
get_eigschur.spectral.Rd

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

Usage

# S3 method for 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)
#>            [,1]       [,2]       [,3]
#> [1,]  0.2222222 -0.1111111 -0.1111111
#> [2,] -0.1111111  0.2222222 -0.1111111
#> [3,] -0.1111111 -0.1111111  0.2222222

# Returns the Schur square of the 2-projector.
get_eigschur(decomp, id1=1, id2=1)
#>           [,1]      [,2]      [,3]
#> [1,] 0.1111111 0.1111111 0.1111111
#> [2,] 0.1111111 0.1111111 0.1111111
#> [3,] 0.1111111 0.1111111 0.1111111

# Also returns the Schur square of the 2-projector
get_eigschur(decomp, id1=1)
#>           [,1]      [,2]      [,3]
#> [1,] 0.1111111 0.1111111 0.1111111
#> [2,] 0.1111111 0.1111111 0.1111111
#> [3,] 0.1111111 0.1111111 0.1111111