Matrices (mathematics)

rectangular array of numbers, symbols, or expressions, arranged in rows and columns

sums of each row, column, and main diagonals are equal

square matrix with ones on the main diagonal and zeros elsewhere

matrix with the same number of rows and columns

matrix equal to its transpose

thumb|200px|right|class=skin-invert-image|The transpose AT of a matrix A can be obtained by reflecting the elements along its main diagonal. Repeating the process on the transposed matrix returns the elements to their original position.

special kind of square matrix

square matrix with non-zero determinant

one of the diagonals of a square matrix

matrices important in quantum mechanics and the study of spin

matrix equal to its conjugate-transpose

complex square matrix whose inverse equals its conjugate transpose

square matrix used to represent a graph or network

matrix whose entries are all 0

the matrix of all first-order partial derivatives of a vector-valued function

complex matrix A* obtained from a matrix A by transposing it and conjugating each entry

real square matrix whose columns and rows are orthogonal unit vectors

square matrix whose transpose is its negative

equivalence relation between matrices

matrix of second derivatives

inverse image of zero under a linear map

matrices representing permutation of vector elements; with exactly one 1 per row and column

structured matrix with equal values along diagonals

matrix defined using smaller matrices called blocks

matrix representing a Euclidean rotation

matrix that commutes with its conjugate transpose

Mathematical concept

endomorphism whose sufficiently large power is zero

matrix that shows the relationship between two classes of objects

measure of covariance of components of a random vector

central object in linear algebra; mapping vectors to vectors

matrix with entries from the Boolean domain B = {0, 1}

matrix used to describe the transitions of a Markov chain

matrix which, when multiplied by itself, yields itself

real square matrix whose all columns (rows) are mutually orthogonal and which only 1 or −1 as entries

matrix obtained by appending the columns of two given matrices

square matrix that has zero entries below the first subdiagonal or has zero entries above the first superdiagonal

matrix representation of a graph

linear transformation that describes a reflection about a plane or hyperplane containing the origin

matrix similar to a diagonal matrix

matrix representation of a Clifford algebra

matrix where every element is equal to one

square matrix whose entries are unit fractions of special form

a square matrix in which each ascending skew-diagonal from left to right is constant

3×3 unitary matrix relating the mass eigenbasis of the three generations of quarks to the basis under which the weak interactions diagonalize

matrix in which the magnitude of the diagonal entry in a row is no less than the sum of the magnitudes of the nondiagonal entries in that row

complex square matrix such that its its conjugate transpose is equal to its negative

matrix of inner products of a set of vectors

function K of the input x of a well-posed problem which describes how much its variation influences the variation of the output g(x)

equivalence relation between matrices

square matrix associated to two univariate polynomials with coefficients in a field or a commutative ring

set of matrices useful in studying the strong force

system for describing optical polarization

matrix satisfying some of the criteria of an inverse

matrix with a specific relation to its characteristic polynomial p

matrices named after Élie Cartan

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 process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT).

matrix in which each row is rotated one position to the right from the previous row

integer matrix whose determinant is 1 or −1

commutative, associative algebra of two complex dimensions