🎓 Deeper Dive — Adults

A matrix is a rectangular array of numbers. Notation: A is m×n (m rows, n columns).

Addition: only for same-shaped matrices, element-wise. Multiplication: A(m×n) × B(n×p) = C(m×p) — inner dimensions must match.

Identity matrix I: 1s on diagonal, 0s elsewhere. AI = IA = A. Determinant 2×2: |ad − bc|. Inverse: A⁻¹ such that A·A⁻¹ = I (exists iff det ≠ 0).

Matrices encode transformations, solve linear equations, and underpin all of machine learning.