




"""simple docstring"""

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	return [
	    txt[:a] + txt[a].upper() + txt[a + 1 :]
	    for a in range(len(_UpperCAmelCase	)	)
	    if txt[a].isalpha()
	]


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











"""simple docstring"""

from typing import Any

import numpy as np

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	return np.array_equal(_UpperCAmelCase  ,      matrix.conjugate().T	)

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	A_  :				Tuple	   =		v.conjugate().T
	A_  :				Tuple	   =		v_star.dot(_UpperCAmelCase	)
	assert isinstance(_UpperCAmelCase  ,      np.ndarray	)
	return (v_star_dot.dot(_UpperCAmelCase	)) / (v_star.dot(_UpperCAmelCase	))

def 		lowercase_      (		):




	"""simple docstring"""






	A_  :				Optional[Any]	   =		np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]]	)
	A_  :				str	   =		np.array([[1], [2], [3]]	)
	assert is_hermitian(_UpperCAmelCase	), f"""{a} is not hermitian."""
	print(rayleigh_quotient(_UpperCAmelCase  ,      _UpperCAmelCase	)	)

	A_  :				int	   =		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()





