Core Idea

• Matrices represent linear maps and batched data.
• Core operations are addition, multiplication, and transpose.

Key Formulas

If $A\in\mathbb{R}^{m\times n}$ and $B\in\mathbb{R}^{n\times p}$, then:

Practical Notes

Check matrix shapes before multiplication.

• Shape mismatch is the most common implementation bug.

Matrix multiplication is not commutative.

• Usually $AB \ne BA$.

Why This Matters for ML

• Every linear layer in neural networks is matrix multiplication plus bias.
• Batched prediction, feature transforms, and covariance calculations all rely on matrix operations.
• Understanding shape rules prevents common implementation and debugging errors in ML code.
• Efficient tensor/matrix operations are central to training speed on GPU hardware.