You're forgetting to append the empty list beforehand. Thus why you get a, IndexError when you try to do arr[i].

arr = []
for i in range(10):
    arr.append([])
    for j in range(5):
        arr[i].append(i*j)

Use np.empty to initialize an empty array and define the axis you want to append across:

import numpy as np
mat = np.empty((0,2))
for i in np.arange(3):
    val = np.random.rand(2, 2)
    mat = np.append(mat,val, axis=0)
print(mat)

Output:

[[0.08527627 0.40567273]
 [0.39701354 0.72642426]
 [0.17540761 0.02579183]
 [0.76271521 0.83032347]
 [0.08105248 0.67986726]
 [0.48079453 0.37454798]]

However, as stated in my comment, if you need to append a lot of times you should look into initializing an array of the correct size then assigning values over using np.append() or appending to a list instead (if you do not know the size of the array) and then creating a numpy array after

You do not "declare" arrays or anything else in python. You simply assign to a (new) variable. If you want a multidimensional array, simply add a new array as an array element.

arr = []
arr.append([])
arr[0].append('aa1')
arr[0].append('aa2')

or

arr = []
arr.append(['aa1', 'aa2'])

You can try this:

import numpy as np
listvals = []
for i in range(10):
    listvals.append((xc, yc))
mat_vals = np.vstack(listvals)

This will output an ndarray like this:

[[ 2  0]
 [ 3  1]
 [ 4  2]
 [ 5  3]
 [ 6  4]
 [ 7  5]
 [ 8  6]
 [ 9  7]
 [10  8]
 [11  9]]

Or this maybe is better:

import numpy as np
list_xc = []
list_yc = []
for i in np.arange(10): 
    list_xc.append(xc)
    list_yc.append(yc)
mat_xc = np.asarray(list_xc)
mat_yc = np.asarray(list_yc)
mat_f = np.column_stack((mat_xc, mat_yc))