Broadcasting & Linear Algebra

What is Broadcasting?

Broadcasting is NumPy's ability to apply operations on arrays of different shapes without making explicit copies.

Rule of Thumb

NumPy compares shapes element-wise from the trailing dimensions forward. Two dimensions are compatible if they are equal or one of them is 1.

# Shape (3, 3) + Shape (3,) → Works!
matrix = np.ones((3, 3))
row = np.array([1, 2, 3])
result = matrix + row  # row is "broadcast" to all 3 rows

Essential Math Operations

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

np.add(a, b)      # Element-wise addition
np.multiply(a, b) # Element-wise multiplication (Hadamard)
np.dot(a, b)      # Dot product (1*4 + 2*5 + 3*6 = 32)

⚠️ Never use * for matrix multiplication. Always use np.dot() or the @ operator.