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🧮 Matrix Multiplication

If you've ever seen an AI paper, you've probably seen W×XW \times X. Matrix multiplication is the absolute workhorse of deep learning.

🚂 The Transformation Engine​

When we multiply our data matrix XX by a weight matrix WW, we are transforming our data (like applying an Instagram filter to a photo).

🤝 The "Handshake" Rule​

You can't just mash any two matrices together. They have to fit perfectly like Lego pieces. If Matrix A is (Rows x Columns) and Matrix B is (Rows x Columns), they can only multiply if A's Columns == B's Rows.

🐍 Python Implementation​

Using numpy, matrix multiplication is done using the @ operator or np.dot().

import numpy as np

# A dataset of 3 items, each with 2 features (3x2 Matrix)
X = np.array([
    [1.0, 2.0],
    [3.0, 4.0],
    [5.0, 6.0]
])

# A weight matrix to transform our 2 features into 1 prediction (2x1 Matrix)
W = np.array([
    [0.5],
    [1.5]
])

# Handshake rule check: (3x2) * (2x1) -> valid! Result will be (3x1)
predictions = X @ W  # Matrix Multiplication!

print("Predictions:\n", predictions)