Fundamental Linear Algebra Objects

la.py

>>> import numpy as np

>>> # Scalars are just a single number.
>>> scalar = 5.0
>>> np.isscalar(scalar)
True

>>> # Vectors are a matrix with one column.
>>> vector = np.arange(10)
>>> vector
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

>>> # Matrices are 2d.
>>> matrix = np.arange(9).reshape((3, 3))
>>> matrix
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
>>> # We need to index these matrices with two values.
>>> first_matrix_element = matrix[0][0]
>>> first_matrix_element
0

>>> # Tensors are n-dimensional matrices.
>>> tensor = np.arange(27).reshape((3, 3, 3))
>>> tensor
array([[[ 0,  1,  2],
        [ 3,  4,  5],
        [ 6,  7,  8]],

       [[ 9, 10, 11],
        [12, 13, 14],
        [15, 16, 17]],

       [[18, 19, 20],
        [21, 22, 23],
        [24, 25, 26]]])
>>> # We can use Python index slicing to efficently get data.
>>> first_row_of_every_dim = tensor[:,0,:]
>>> first_row_of_every_dim
array([[ 0,  1,  2],
       [ 9, 10, 11],
       [18, 19, 20]])