"""simple docstring"""





def      lowerCamelCase_(__SCREAMING_SNAKE_CASE  )->    int:

							if not isinstance(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  ):
														raise TypeError("""only integers accepted as input"""  )
							else:
														_SCREAMING_SNAKE_CASE		:						List[Any]			  =    str(abs(__SCREAMING_SNAKE_CASE  )  )
														_SCREAMING_SNAKE_CASE		:						List[str]			  =    [list(__SCREAMING_SNAKE_CASE  ) for char in range(len(__SCREAMING_SNAKE_CASE  )  )]
														for index in range(len(__SCREAMING_SNAKE_CASE  )  ):
																					num_transpositions[index].pop(__SCREAMING_SNAKE_CASE  )
														return max(
														    int("""""".join(list(__SCREAMING_SNAKE_CASE  )  )  ) for transposition in num_transpositions  )


if __name__ == "__main__":
			__import__('''doctest''').testmod()



"""simple docstring"""





from typing import Any

import numpy as np



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE  )->    bool:
							return np.array_equal(__SCREAMING_SNAKE_CASE     ,	matrix.conjugate().T  )



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )->    Any:
							_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    v.conjugate().T
							_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    v_star.dot(__SCREAMING_SNAKE_CASE  )
							assert isinstance(__SCREAMING_SNAKE_CASE     ,	np.ndarray  )
							return (v_star_dot.dot(__SCREAMING_SNAKE_CASE  )) / (v_star.dot(__SCREAMING_SNAKE_CASE  ))



def      lowerCamelCase_()->    None:
							_SCREAMING_SNAKE_CASE		:						Optional[Any]			  =    np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]  )
							_SCREAMING_SNAKE_CASE		:						int			  =    np.array([[1], [2], [3]]  )
							assert is_hermitian(__SCREAMING_SNAKE_CASE  ), F"""{a} is not hermitian."""
							print(rayleigh_quotient(__SCREAMING_SNAKE_CASE     ,	__SCREAMING_SNAKE_CASE  )  )

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


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			tests()


