a , b = var('a, b')

A = matrix([[a,b],[-b,a]])

print A


A.characteristic_polynomial()

A.eigenvalues()

#moduli of the eigenvalues = sqrt(a^2 + b^2)

# b = 0 => the matrix is symmetric 

# a = 0 => the matrix is not skew-symmetric

# sqrt(a^2 + b^2) = 1 => the matrix is orthogonal

SageDays/Kreyszig-7.3-2 (last edited 2010-08-11 12:52:58 by bhanukiran)