Foreword

In Numpy, array is used to represent general-purpose N-dimensional arrays, and matrix is used specifically for linear algebra calculations. Both two-dimensional array and matrix can be used to represent matrices, but there are some differences between the two when multiplication is performed.

The operation of Array is to operate on each element, and the operation of Matrix is to operate on the matrix.

Constant multiplication of List and Numpy array

We can see that when a list performs a constant multiplication operation, the original list is repeatedly concatenated by N times. To perform individual operations on each element, a for loop iteration needs to be used, because the list has the characteristics of heterogeneous data types. And ndarray will directly multiply each element by N multiples during the multiplication of constants, which is the performance of ndarray homogeneous data type.

list_1 = [[1, 2], [3, 4]]
x = np.array(list_1)

print(list_1*3)
print('\n')
print()
print('\n')
print(x*3)

# output
# print(list_1*3)
[[1, 2], [3, 4], [1, 2], [3, 4], [1, 2], [3, 4]]

# print(x) 
[[1 2]
 [3 4]]

# print(x*3)
 [[ 3  6]
 [ 9 12]]

Quantity product (dot product) and vector product (cross product) of Numpy array

We can see that the result of Numpy’s array operation using * is the product of quantities, while the result of operation using the function dot() is the product of vectors:


list_1 = [[1, 2], [3, 4]]
list_2 = [[5, 6], [7, 8]]
x = np.array(list_1)
y = np.array(list_2)

print('x * y =',x*y)
print('\n')
print('np.dot(x, y) =',np.dot(x,y))

# output
# array using *
x * y =
 [[ 5 12]
 [21 32]]

# array using method dot()
np.dot(x, y) =
 [[19 22]
 [43 50]]

Transpose of Numpy array

When transposing a one-dimensional array through Numpy array, the result is the same:

z = np.array([1, 2, 3, 4])

print(z)
print(z.T)

# output
# print(z)
[1 2 3 4]
# print(z.T)
[1 2 3 4]

Multiplication of List and Numpy matrix

Similarly, when a matrix performs a constant multiplication operation, each element is multiplied by a multiple of the constant:

list_1 = [[1, 2], [3, 4]]
x = np.matrix(list_1)

print(x)
print('\n')
print(x*3)

# output
# print(x)
[[1 2]
 [3 4]]

# print(x*3)
[[ 3  6]
 [ 9 12]]

Quantity product (dot product) and vector product (cross product) of Numpy matrix

Unlike arrays, when a matrix is operated on with *, the result is a vector product, while a multiply() operation results in a quantitative product:

list_1 = [[1, 2], [3, 4]]
list_2 = [[5, 6], [7, 8]]
x = np.matrix(list_1)
y = np.matrix(list_2)

print('x * y =\n',x*y)
print('\n')
print('np.dot(x, y) =\n',np.dot(x, y))

# output
# matrix using * 
x * y =
 [[19 22]
 [43 50]]

# matrix using multiply()
np.multiply(x, y) = 
 [[ 5 12]
 [21 32]]

transpose of Numpy matrix

When transposing a one-dimensional array through Numpy array, the result is not the same as the transposing result of array:

list_3 = [1, 2, 3, 4]
z = np.matrix(list_3)

print(z)
print(z.T)

# output
# print(z)
[[1, 2, 3, 4]]
# print(z.T)
[[1]
 [2]
 [3]
 [4]]