"""simple docstring"""






from typing import Any

import numpy as np




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase       )							->   bool:
				return np.array_equal(__UpperCAmelCase  ,					matrix.conjugate().T       )




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase  ,					__UpperCAmelCase       )							->   Any:
				SCREAMING_SNAKE_CASE__		  =				v.conjugate().T
				SCREAMING_SNAKE_CASE__		  =				v_star.dot(__UpperCAmelCase       )
				assert isinstance(__UpperCAmelCase  ,					np.ndarray       )
				return (v_star_dot.dot(__UpperCAmelCase       )) / (v_star.dot(__UpperCAmelCase       ))




def 						SCREAMING_SNAKE_CASE					(  )							->   None:
				SCREAMING_SNAKE_CASE__		  =				np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]]       )
				SCREAMING_SNAKE_CASE__		  =				np.array([[1], [2], [3]]       )
				assert is_hermitian(__UpperCAmelCase       ), F"""{a} is not hermitian."""
				print(rayleigh_quotient(__UpperCAmelCase  ,					__UpperCAmelCase       )       )

				SCREAMING_SNAKE_CASE__		  =				np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]       )
				assert is_hermitian(__UpperCAmelCase       ), F"""{a} is not hermitian."""
				assert rayleigh_quotient(__UpperCAmelCase  ,					__UpperCAmelCase       ) == float(3       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						tests()





"""simple docstring"""






from math import pi




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase  ,					__UpperCAmelCase       )							->   float:
				return 2 * pi * radius * (angle / 360)


if __name__ == "__main__":
						print(arc_length(9_0, 1_0))




