||'''Book'''|| Advanced Engineering Mathematics ||
 ||'''Author'''|| Erwin Kreyszig ||
 ||'''Edition'''|| 8th Edition ||

/* code_begins */

{{{
theta= var('theta')

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

print A


A.characteristic_polynomial()

evals = A.eigenvalues()
print 'eigenvalues are'
print evals



a = vector([-sin(theta), cos(theta)])
b = vector([-sin(theta), +cos(theta)])

a*b

# one of the eigenvalues is real, two are complex conjugate pairs and their absolute = 1 => orthogonal matrix

}}}

/* code_ends */

 * '''Solution by''': 
  * ganesh, developer, space
  * bhanukiran, student, technical university of Delft
  * saransh, student, sobhit university
  * ujwala, lecturer, aurangabad