Researched
Linear Algebra & Matrices
Cayley's matrix algebra (1858) gives a compact calculus for systems of equations, rotations and transformations.
Open in the interactive tree →Solving many equations at once goes back to ancient Chinese methods and Gauss's elimination; Grassmann (1844) and Cayley (1858) built the abstract theory of vectors and matrices. Heisenberg's quantum mechanics (1925) was soon recognised as matrix algebra. Today every graphics chip and neural network is essentially a machine for multiplying matrices.
Prerequisites
- Nine Chapters (China)~100 ADThe 'fangcheng' method of the Nine Chapters is Gaussian elimination, the core of linear algebra
- Zero, Decimals & Algebra~820
- Number Theory & Group Theory1801
Unlocks
- Abstract Algebra (Noether)1921-1931
- Quantum Mechanics1925Heisenberg's matrix mechanics (1925) is built on matrix algebra
- Linear Optimization (Simplex)1947The simplex method works by pivoting on systems of linear equations
- Kalman Filter1960
- Deep Learning2012Neural networks are layers of matrix multiplications
- Sphere Packing in 8 & 24 Dims2016