son's method.ipynb

Kernel: SageMath 8.2

%display latex

theta, phi, psi = var('theta, phi, psi')

R1 = matrix([[cos(phi),-sin(phi),0],[sin(phi),cos(phi),0],[0,0,1]]); R1

R2 = matrix([[1,0,0],[0,cos(theta),-sin(theta)],[0,sin(theta),cos(theta)]]); R2

Lambda = R1.apply_map(lambda x: x(phi=phi-pi/2))*R2.apply_map(lambda x: x(theta=-theta)); Lambda.simplify_full()

(Lambda*Lambda.transpose()).simplify_trig()

e = [matrix([[1,0,0],[0,-1,0],[0,0,0]]), matrix([[0,1,0],[1,0,0],[0,0,0]])]; e

for i in range(2):
    show((Lambda.transpose()*e[i]*Lambda).simplify_trig())

for i in range(2):
    show((Lambda*e[i]*Lambda.transpose()).simplify_trig())