SpectralRadius

Returns the spectral radius of a square matrix.

Syntax

• SpectralRadius(A)

  • A is a square matrix

Description

If A is a square matrix, then SpectrialRadius(A) returns the spectral radius of A, that is, the greatest absolute value amongst the eigenvalues of A.

Thus,

SpectralRadius(A) = max(spectrum(A) @ abs)

Examples

A ≔ ❨❨5, 0, 2, 3, 1❩, ❨1, 4, 0, 1, 0❩, ❨0, 5, 8, 3, 1❩, ❨−1, 2, 5, 3, 6❩, ❨1, 5, 3, 2, 0❩❩

⎛ 5   0   2   3   1⎞
⎜ 1   4   0   1   0⎟
⎜ 0   5   8   3   1⎟
⎜−1   2   5   3   6⎟
⎝ 1   5   3   2   0⎠

SpectralRadius(A)

12.0996507021

See also

• eigenvalues

• spectrum