🎓 Chapter 9: Linear Algebra & Matrix Math
APL was originally created as a mathematical notation for linear algebra and array manipulation.
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1. Matrix Multiplication with Inner Product (A +.× B)
The Inner Product operator (A f.g B) generalizes dot products.
When instantiated as +.×, it performs standard linear algebra Matrix Multiplication:
C[i, j] = sum(A[i, k] × B[k, j])
A ← 2 2 ⍴ 1 2 3 4
B ← 2 2 ⍴ 5 6 7 8
⍝ Compute matrix product A +.× B
A +.× B---
2. Matrix Inversion & Domino Operator (⌹)
The Domino primitive (⌹) handles matrix inverses and linear system solvers:
- Monadic Matrix Inverse (
⌹ M): Calculates the inverse matrix M⁻¹. - Dyadic Linear Solver (
B ⌹ A): Solves the system of equations A · x = B.
Example:
Solve the simultaneous equations:
2x + y = 5
x + 3y = 10
A ← 2 2 ⍴ 2 1 1 3
B ← 5 10
⍝ Solve for vector x = [x, y]
B ⌹ A← Chapter 8: Sorting (⍋ ⍒), Grouping (⌸) & Data Manipulation Chapter 10: Conway's Game of Life & Fractals in APL →