Thanks Edmondo, Stephen, Mats and Steven you for the tips,
I studied linear algebra many years ago and I remember only a few rudiments.
But I was trying to visualize (in a geometric way) how the numpy
represents arrays, and what the geometrical meaning of the transpose
operation made by numpy.
I think I understood a little bit more.
The number of nested brackets indicates the number of array dimensions.
the vector ( [1,2] ) is one-dimensional, but the vector ( [ [1,2] ] ) is
two-dimensional.
v_1 = np.array( [1,2] )
> v_1.shape
(2,)
> v_1
v_1
> v_1
array( [1, 2] )
> v_2 = np.array( [ [1,2] ] )
> v_2.shape
(1, 2)
And it does not make sense to transpose a one-dimensional array.
> v_1.T
array( [1, 2] )
> v_2.T
array( [ [1],
[2] ] )
Anothe example:
vector_1 = np.array( [ 1, 2, 3, 4, 5, 6, 7, 8 ] )
^
vector_2 = np.array( [ [1, 2, 3, 4], [5, 6, 7, 8] ] )
^ ^
vector_3 = np.array( [ [ [1,2], [3,4] ], [ [5,6], [7,8] ] ] )
^ ^ ^
> vector_1
array([1, 2, 3, 4, 5, 6, 7, 8])
> vector_2
array( [ [1, 2, 3, 4],
[5, 6, 7, 8] ] )
> vector_3
array( [ [ [1, 2],
[3, 4] ],
[ [5, 6],
[7, 8] ] ] )
And looking for some tutorial about geometric aspects of matrices and
the geometric meaning of the transpose I found that transposed is
"mirrored along the diagonal" at:
https://www.coranac.com/documents/geomatrix/
>vector_1.T
array([1, 2, 3, 4, 5, 6, 7, 8])
> vector_2.T
array( [ [1, 5],
[2, 6],
[3, 7],
[4, 8] ] )
> vector_3.T
array( [ [ [1, 5],
[3, 7]],
[ [2, 6],
[4, 8] ] ] )
Thank you,
Markos
Em 21-06-2019 07:44, edmondo.giovanno...@gmail.com escreveu:
Every array in numpy has a number of dimensions,
"np.array" is a function that can create an array numpy given a list.
when you write
vector_1 = np.array([1,2,1])
you are passing a list of number to thet function array that will create a 1D
array.
As you are showing:
vector_1.shape
will return a tuple with the sizes of each dimension of the array that is:
(3,)
Note the comma thta indicate that is a tuple.
While if you write:
vector_2 = np.array([[1,2,3]])
You are passing a list of list to the function array that will instruct it to
crete a 2D array, even though the size of the first dimension is 1:
vector_2.shape
(1,3)
It is still a tuple as you can see.
Try:
vector_3 = np.array([[1,2,3],[4,5,6]])
And you'll see that i'll return a 2D array with a shape:
vector_3.shape
(2,3)
As the external list has 2 elements that is two sublists each with 3 elements.
The vector_2 case is just when the external list has only 1 element.
I hope it is more clear now.
Cherrs,
Il giorno venerdì 21 giugno 2019 08:29:36 UTC+2, Markos ha scritto:
Hi,
I'm studying Numpy and I don't understand the difference between
vector_1 = np.array( [ 1,0,1 ] )
with 1 bracket and
vector_2 = np.array( [ [ 1,0,1 ] ] )
with 2 brackets
The shape of vector_1 is:
vector_1.shape
(3,)
But the shape of vector_2 is:
vector_2.shape
(1, 3)
The transpose on vector_1 don't work:
vector_1.T
array([1, 0, 1])
But the transpose method in vector_2 works fine:
vector_2.T
array([[1],
[0],
[1]])
I thought that both vectors would be treated as an matrix of 1 row and 3
columns.
Why this difference?
Any tip?
Thank you,
Markos
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