mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices generate...

Binary matrix (zero-one matrix) Elementary matrix Exchange matrix Matrix of ones Pauli matrices (the identity matrix is the zeroth Pauli matrix) Householder...

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...

linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the...

classes of elementary matrix is involutory, namely the row-interchange elementary matrix. A special case of another class of elementary matrix, that which...

invertible matrix. The method is named after Carl Friedrich Gauss (1777–1855). To perform row reduction on a matrix, one uses a sequence of elementary row operations...

a shear matrix or transvection, an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived...

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices...

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

expressed as a finite product of elementary matrices. Furthermore, the following properties hold for an invertible matrix A: ( A − 1 ) − 1 = A {\displaystyle...

In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows and columns...

In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U−1 equals its conjugate transpose U*, that is, if U ∗ U = U...

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...

-dimensional matrix A {\displaystyle A} . This is usually done for the purpose of performing the same elementary row operations on the augmented matrix ( A |...

column. The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations used to obtain it. The variant...

A Frobenius matrix is a special kind of square matrix from numerical analysis. A matrix is a Frobenius matrix if it has the following three properties:...

(Conder, Robertson & Williams 1992, p. 19). Let Tij := eij(1) be the elementary matrix with 1's on the diagonal and in the ij position, and 0's elsewhere...

approach to finding the rank of a matrix is to reduce it to a simpler form, generally row echelon form, by elementary row operations. Row operations do...

In mathematics, an anti-diagonal matrix is a square matrix where all the entries are zero except those on the diagonal going from the lower left corner...

one replaces Tietze moves for the fundamental group presentation by elementary matrix operations for the presentation matrices for H n ( X ; Z ) {\displaystyle...

square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is...

the elementary divisors of A; these can be immediately read off from a matrix in Jordan form, but they can also be determined directly for any matrix by...

Internet industry association Elementary column operations, an operation performed on the columns of an elementary matrix in mathematics Engineering change...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

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 = [...

adjugate of a square matrix A is the transpose of its cofactor matrix and is denoted by adj(A). It is also occasionally known as adjunct matrix, or "adjoint"...

values, so 1 + 1 = 0 {\displaystyle 1+1=0} ), which expresses the elementary matrix of switching two rows (or columns) in terms of the transvections (shears)...

definiteness of a symmetric real matrix. Namely, the matrix is reduced to an upper triangular matrix by using elementary row operations, as in the first...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

pp. 536, 7, ISBN 978-0-471-50447-4 Ch.VII, §7.2 Howard Eves (1966) Elementary Matrix Theory, § 5.4A Cayley’s Construction of Real Orthogonal Matrices,...