In physics, the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering...

replacing it with abstract mathematical properties of the S-matrix. In S-matrix theory, the S-matrix relates the infinite past to the infinite future in one...

computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices...

In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices...

theory where they can be used to calculate various observables such as S-matrix elements, although they are not themselves observables. This is because...

invertible matrix (non-singular, non-degenarate or regular) is a square matrix that has an inverse. In other words, if some other matrix is multiplied...

\phi } 's if one uses the S-matrix to swap the two ψ {\displaystyle \psi } 's. Identifying the coefficients of the ϕ {\displaystyle \phi } 's on both...

In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows...

outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 following John Archibald Wheeler's 1937 introduction of the S-matrix. Many...

columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number...

covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the...

algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions;...

The Matrix is an American cyberpunk media franchise consisting of four feature films, beginning with The Matrix (1999) and continuing with three sequels...

Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks...

implies the S-matrix is 1, no interaction occur and all states remain unchanged. Unitarity of the S-matrix: S † S = 1 {\displaystyle S^{\dagger }S=1} is then...

property requires the S-matrix to factorize S β α → S β 1 α 1 S β 2 α 2 {\displaystyle S_{\beta \alpha }\rightarrow S_{\beta _{1}\alpha _{1}}S_{\beta _{2}\alpha...

or in the related S {\displaystyle S} -matrix. In the case of the Coulomb potential considered above this S {\displaystyle S} -matrix is given by the following...

in the Matrix franchise to be directed solely by Lana. It is the sequel to The Matrix Revolutions (2003) and the fourth installment in The Matrix film series...

particles or fields. The transition amplitude is then given as the matrix element of the S-matrix between the initial and final states of the quantum system....

in terms of the S-matrix. Here δ is the Dirac delta function. The computation of the S-matrix is the main goal of the scattering theory...

In linear algebra, a completely-S matrix is a square matrix such that for every principal submatrix R there exists a positive vector u such that Ru >...

Weisskopf, and others. Related theories are U-matrix, S-matrix, by M-matrix, or T-matrix. The term R-matrix is used in connection with the Yang–Baxter equation...

first formulated by Steven Weinberg in 1965, allows calculation of the S-matrix, used in calculating the outcome of collisions between particles, when...

linear algebra, a square matrix A {\displaystyle A}  is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists...

abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The set...

A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links...

rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [...

scattering of fundamental particles is described by the Scattering Matrix or S-Matrix, introduced and developed by John Archibald Wheeler and Werner Heisenberg...

for the S-matrix: M f i = ( i e ) 2 u ¯ ( p → ′ , s ′ ) ϵ / ′ ( k → ′ , λ ′ ) ∗ p / + k / + m e ( p + k ) 2 − m e 2 ϵ / ( k → , λ ) u ( p → , s ) + ( i...

if A = S B S ¯ − 1 {\displaystyle A=SB{\bar {S}}^{-1}\,} for some invertible n × n {\displaystyle n\times n} matrix S {\displaystyle S} , where S ¯ {\displaystyle...