Operations

We are able to use a couple of operators to perform various operations on Matrix instances.

from basic_deep_learning import*

A = Matrix([[1, 2, -4], [2, 0, 1]])
B = Matrix([[6, -1, 3], [2, 1, 0]])

print(f"A + B = {A + B}")  #Addition
print(f"A - B = {A - B}")  #Substraction
print(f"A @ B = {A @ B}")  #Component-wise multiplication
print(f"3 * A = {3 * A}") #Scaling
print(f"B / 4 = {B / 4}") #Component-wise division

A + B = matrix([
        [7.0, 1.0, -1.0],
        [4.0, 1.0, 1.0]
])
A - B = matrix([
        [-5.0, 3.0, -7.0],
        [0.0, -1.0, 1.0]
])
A @ B = matrix([
        [6.0, -2.0, -12.0],
        [4.0, 0.0, 0.0]
])
3 * A = matrix([
        [3.0, 6.0, -12.0],
        [6.0, 0.0, 3.0]
])
B / 4 = matrix([
        [1.5, -0.25, 0.75],
        [0.5, 0.25, 0.0]
])

Performing an addition, substraction or component-wise multiplication between two matrices who do not have the same format will raise a TypeError.

Once the number of columns of the first matrix is equal to the number of rows of the second, we can perform matrix multiplication.

from basic_deep_learning import*

A = Matrix([[1, 2, -4], [2, 0, 1]])
B = Matrix([[-1, 0, 1, 2], [0, 1, 2, -1], [1, 2, -1, 0]])

print(A * B)

matrix([
        [-5.0, -6.0, 9.0, 0.0],
        [-1.0, 2.0, 1.0, 4.0]
])

But print(B * A) yields:

TypeError: Invalid matrix formats (4≠2).

Definition:

T() -> Self

The T() method takes no arguments and simply returns the tranposed matrix.

print(A.T())

matrix([
        [1, 2],
        [2, 0],
        [-4, 1]
])

Finally, we can use the == operator between Matrix instances; A == B is True if, and only if their matrix attributes are equal.