Is Matrix Multiplication Ugly?
a day ago
- #mathematics
- #artificial intelligence
- #linear algebra
- The author critiques a New Yorker article by Stephen Witt for misrepresenting matrix multiplication as lacking beauty and symmetry.
- Matrix algebra is defended as a language of symmetry and transformation, essential in various fields like AI, physics, and economics.
- The non-commutative nature of matrix multiplication (AB ≠ BA) is compared to other operations where order matters, like composing music or making a salad.
- The article explains that matrices represent transformations, not just arrays of numbers, and their composition (multiplication) is a fundamental concept in linear algebra.
- The author argues that the tedium of manual matrix multiplication doesn't detract from its mathematical elegance and utility.
- G.H. Hardy's preference for conceptual proofs over brute-force calculations is discussed, but the author clarifies that this doesn't diminish the value of matrix operations in applied mathematics.
- The piece concludes by distinguishing the repetitive computational tasks from the underlying beauty and importance of matrix theory in mathematics and science.