QR decomposition

LU decomposition

LU decomposition factors a matrix as the product of a lower triangular matrix and an upper triangular matrix

Cholesky decomposition

Cholesky decomposition factors A = LL^T for symmetric positive definite matrices

Shor's algorithm

Shor's algorithm factors integers in polynomial time on a quantum computer

Vector quantization

Product quantization compresses vectors by splitting them into subvectors and quantizing each subvector independently

RoPE encodes position: multiply Q,K by rotation matrix R(θ_i) at each position

RoPE encodes position by multiplying Q,K by R(θ_i) at each position

orthogonal matrices preserve distances: O^T O = I means no stretching or squashing

Orthogonal matrices preserve distances because O^T O = I ensures no stretching or squashing occurs