dividing by list not possible?

[volcano63]

Also, I think the numpy authors were trying to emulate matrix operations. Mathematicians don't divide matrices, mainly because matrix multiplication is not commutative, leading to an ambiguous definition of the inverse operation.

Dividing and multiplying numpy.array is possible

Output:
In [19]: N=500
    ...: R=0.5
    ...: 
    ...: pressure_list=np.array([16,25,40])
    ...: expectation_val_V=np.array([445.186, 412.284, 390.5])
    ...: expectation_eta=(4/3 *np.pi *R**3)/expectation_val_V
    ...: 
    ...: 

In [20]: expectation_eta
Out[20]: array([0.00117613, 0.00127   , 0.00134084])

Elements of numpy.array all have the same type

Output:
In [24]: pressure_list.dtype
Out[24]: dtype('int64')

and if the dtype of an array allows for math operation (as long as shapes of arrays are compatible) - you are free to apply math operations on arrays.

Output:
In [51]: np.reshape(np.arange(6), (2, 3)) * np.arange(6, 9)
Out[51]: 
array([[ 0,  7, 16],
       [18, 28, 40]])

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list in Python is agnostic of the type of elements - which (element(s)) may be replaced by element(s) of another type dynamically, therefor math operations between lists (excluding addition - below) are meaningless.

List addition is basically interpreted as list concatenation

Output:
In [22]: list.__add__?
Signature:      list.__add__(self, value, /)
Call signature: list.__add__(*args, **kwargs)
Type:           wrapper_descriptor
String form:    <slot wrapper '__add__' of 'list' objects>
Namespace:      Python builtin
Docstring:      Return self+value.

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PS

numeric numpy.array may also be multiplied or divided by a scalar digital value; power op is applicable too

Output:
In [52]: np.arange(6, 9) ** 2
Out[52]: array([36, 49, 64])

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PPS
WHat is inefficient - from any point of view - is the calculation of the expression below several times; redundant brackets - together with lack of spaces - reduce readability too
(4*(1-(3*np.sqrt(2))/(np.pi)*eta))