Smatrix

SMatrix is a term used in multiple domains to denote different concepts, most prominently in physics and computer science. In physics, SMatrix commonly refers to the S-matrix, or scattering matrix, a mathematical object that encodes the probabilities of transitions between asymptotic states in particle interactions. The S-matrix links incoming particles before an interaction to outgoing particles after it, with elements called scattering amplitudes. Key properties include unitarity (probabilities are conserved) and, in relativistic theories, Lorentz invariance. The S-matrix framework underpins much of collider phenomenology, enabling calculation of cross sections and decay rates. Historically, it played a central role in the S-matrix program of the mid-20th century, which sought to describe strong interactions using observable quantities rather than detailed Lagrangians. While the program evolved with quantum field theory, the S-matrix remains a foundational concept in scattering theory and theoretical discussions of analyticity and crossing symmetry.

In programming and numerical mathematics, SMatrix often designates a type for statically sized matrices. Notably in the Rust ecosystem’s nalgebra library, SMatrix<T, R, C> represents a fixed-size matrix with R rows and C columns, and element type T. This design enables compile-time dimension checks and stack-allocated storage, which can improve performance for small, dense matrices. SMatrix is typically used alongside SVector for fixed-size vectors. While the naming convention appears in several libraries across languages, the common idea is the same: a matrix whose dimensions are known at compile time rather than at runtime.

See also S-matrix, scattering theory, nalgebra, fixed-size matrices.