eigenkronecker {robustsur}

Spectral Decomposition of a kronecker product of a matrix with an identity matrix

Description

Computes eigenvalues and eigenvectors of the kronecker product of a matrix with an identity matrix.

Usage

eigenkronecker(x, n)

Arguments

x

a numeric or complex symmetric matrix whose spectral decomposition is to be computed. Logical matrices are coerced to numeric.

n

dimension of the identity matrix.

Details

Only symmetric matrices are considered.

Value

The spectral decomposition of kronecher product between x and an identity matrix of dimesion n is returned as a list with components

values

a vector containing the eigenvalues.

vectors

a matrix whose columns contain the eigenvectors.

Author(s)

Claudio Agostinelli and Giovanni Saraceno

References

R.A. Horn and C.R. Johnson (1994) Topics in Matrix Analysis, Cambridge University Press. Theorem 4.2.12.

See Also

eigen and kronecker.

Examples

 eigenkronecker(x=cbind(c(1,-1), c(-1,1)), n=2)