Im a newbie to Numpy and trying to understand the basic question of what is dimension,

I tried the following commands and trying to understand why the ndim for last 2 arrays are same?

>>> a= array([1,2,3])
>>> a.ndim
1
>>> a= array([[1,2,3],[4,5,6]])
>>> a
array([[1, 2, 3],[4, 5, 6]])
>>> a.ndim
2
>>> a=arange(15).reshape(3,5)
>>> a.ndim
2>>> a
array([[ 0,  1,  2,  3,  4],[ 5,  6,  7,  8,  9],[10, 11, 12, 13, 14]])

My understanding..

Case 1:array([[1, 2, 3],[4, 5, 6]])2 elements are present in main lists, so ndim is-2Case 2:array([[ 0,  1,  2,  3,  4],[ 5,  6,  7,  8,  9],[10, 11, 12, 13, 14]])

3 elements are present in the main lists, do ndim is-3

The shape of an array is a tuple of its dimensions. An array with one dimension has a shape of (n,). A two dimension array has a shape of (n,m) (like your case 2 and 3) and a three dimension array has a shape of (n,m,k) and so on.

Therefore, whilst the shape of your second and third example are different, the no. dimensions is two in both cases:

>>> a= np.array([[1,2,3],[4,5,6]])
>>> a.shape
(2, 3)>>> b=np.arange(15).reshape(3,5)
>>> b.shape
(3, 5)

If you wanted to add another dimension to your examples you would have to do something like this:

a= np.array([[[1,2,3]],[[4,5,6]]])

or

np.arange(15).reshape(3,5,1)

You can keep adding dimensions in this way:

One dimension:

>>> a = np.zeros((2))
array([ 0.,  0.])
>>> a.shape
(2,)
>>> a.ndim
1

Two dimensions:

>>> b = np.zeros((2,2))
array([[ 0.,  0.],[ 0.,  0.]])
>>> b.shape
(2,2)
>>> b.ndim
2

Three dimensions:

>>> c = np.zeros((2,2,2))
array([[[ 0.,  0.],[ 0.,  0.]],[[ 0.,  0.],[ 0.,  0.]]])
>>> c.shape
(2,2,2)
>>> c.ndim
3

Four dimensions:

>>> d = np.zeros((2,2,2,2))
array([[[[ 0.,  0.],[ 0.,  0.]],[[ 0.,  0.],[ 0.,  0.]]],[[[ 0.,  0.],[ 0.,  0.]],[[ 0.,  0.],[ 0.,  0.]]]])
>>> d.shape
(2,2,2,2)
>>> d.ndim
4