





from typing import Any

import numpy as np

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

def    lowerCamelCase_(lowerCamelCase_    ,   lowerCamelCase_    ) ->       Any:
						UpperCAmelCase         =     v.conjugate().T
						UpperCAmelCase         =     v_star.dot(__snake_case    )
						assert isinstance(__snake_case    ,   np.ndarray    )
						return (v_star_dot.dot(__snake_case    )) / (v_star.dot(__snake_case    ))

def    lowerCamelCase_() ->       None:
						UpperCAmelCase         =     np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]]    )
						UpperCAmelCase         =     np.array([[1], [2], [3]]    )
						assert is_hermitian(__snake_case    ), F'{a} is not hermitian.'
						print(rayleigh_quotient(__snake_case    ,   __snake_case    )    )

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		tests()








def    lowerCamelCase_(lowerCamelCase_    ) ->       list[int]:
						UpperCAmelCase         =     len(lowerCamelCase_    )
						for i in range(lowerCamelCase_    ):
												for j in range(i + 1    ,   lowerCamelCase_    ):
																		if numbers[j] < numbers[i]:
																								UpperCAmelCase       ,		UpperCAmelCase         =     numbers[j], numbers[i]
						return numbers


if __name__ == "__main__":
		__lowerCamelCase     :							int  							=				input("Enter numbers separated by a comma:\n").strip()
		__lowerCamelCase     :							Dict  							=				[int(item) for item in user_input.split(",")]
		print(exchange_sort(unsorted))



