Matrix Multiplication using Functions in Python

Here’s how you can do Matrix Multiplication using Functions in Python 🧮✨—with step-by-step explanation, code, and practice!

🚦 Step-by-Step Modular Matrix Multiplication

1️⃣ Understand the Problem

• You want to multiply two matrices, A and B.
• A must have as many columns as B has rows.
• Result is a new matrix C.

2️⃣ Break Down the Problem into Functions

Let’s build helper functions:

• row(M, i): returns the ith row of matrix M.
• column(M, j): returns the jth column of matrix M.
• dot(u, v): returns the dot product of two lists u and v.
• matmul(A, B): returns the product of matrices A and B.

3️⃣ Code Implementation

# Get the ith row
def row(M, i):
    return M[i]

# Get the jth column
def column(M, j):
    return [M[k][j] for k in range(len(M))]

# Dot product of two lists
def dot(u, v):
    return sum(u[k] * v[k] for k in range(len(u)))

# Matrix multiplication
def matmul(A, B):
    n = len(A)         # Number of rows in A (assume square for simplicity)
    m = len(B[^0])      # Number of columns in B
    C = []
    for i in range(n):
        row_result = []
        for j in range(m):
            rowA = row(A, i)
            colB = column(B, j)
            row_result.append(dot(rowA, colB))
        C.append(row_result)
    return C

# Example matrices
A = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]
B = [
    [1, 2, 1],
    [3, 1, 7],
    [6, 2, 3]
]
result = matmul(A, B)
for r in result:
    print(r)
# Output:
# [25, 12, 28]
# [55, 27, 64]
# [85, 42, 100]

This modular approach makes your code easy to read and debug!¹

🏋️‍♂️ Practice Question

Q: Multiply these 2x2 matrices using functions:

X = [
    [2, 4],
    [3, 4]
]
Y = [
    [1, 2],
    [1, 3]
]

def row(M, i):
    return M[i]

def column(M, j):
    return [M[k][j] for k in range(len(M))]

def dot(u, v):
    return sum(u[k] * v[k] for k in range(len(u)))

def matmul(A, B):
    n = len(A)
    m = len(B[^0])
    C = []
    for i in range(n):
        row_result = []
        for j in range(m):
            rowA = row(A, i)
            colB = column(B, j)
            row_result.append(dot(rowA, colB))
        C.append(row_result)
    return C

X = [
    [2, 4],
    [3, 4]
]
Y = [
    [1, 2],
    [1, 3]
]
result = matmul(X, Y)
for r in result:
    print(r)
# Output:
# [6, 16]
# [7, 18]

⭐ Key Points

• Modular functions make your code clear and reusable.
• Always check the dimensions before multiplying!
• This approach works for both square and rectangular matrices.

Now you can multiply matrices in Python using functions—try your own examples! 🚀 [Source: Python-IITM-Foundational-Course.pdf]¹