Spectral Radius

Computes the spectral radius of a square matrix, defined as the maximum modulus (absolute value) of its eigenvalues. The spectral radius is often used to assess the stability of systems such as vector autoregressive (VAR) models: a system is considered stationary if the spectral radius of its transition matrix is strictly less than 1.

Usage

SpectralRadius(x)

Arguments

x

Numeric square matrix.

Value

Numeric value representing the spectral radius of x.

See also

Other Simulation of State Space Models Data Functions: LinSDE2SSM(), LinSDECovEta(), LinSDECovY(), LinSDEMeanEta(), LinSDEMeanY(), ProjectToHurwitz(), ProjectToStability(), SSMCovEta(), SSMCovY(), SSMMeanEta(), SSMMeanY(), SimAlphaN(), SimBetaN(), SimBetaN2(), SimCovDiagN(), SimCovN(), SimIotaN(), SimNuN(), SimPhiN(), SimPhiN2(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), TestPhi(), TestPhiHurwitz(), TestStability(), TestStationarity()

Author

Ivan Jacob Agaloos Pesigan

Examples

# Matrix with eigenvalues less than 1
x <- matrix(
  data = c(
    0.5, 0.3,
    0.2, 0.4
  ),
  nrow = 2
)
SpectralRadius(x)
#> [1] 0.7

# Matrix with eigenvalues greater than 1
y <- matrix(
  data = c(
    1.2, 0.3,
    0.4, 0.9
  ),
  nrow = 2
)
SpectralRadius(y)
#> [1] 1.427492