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

algebra, an invertible matrix (non-singular, non-degenerate or regular) is a square matrix that has an inverse. In other words, if a matrix is invertible, it...

Such a matrix is also called a Frobenius matrix, a Gauss matrix, or a Gauss transformation matrix. A block triangular matrix is a block matrix (partitioned...

\end{aligned}}} In block matrix form, we can consider the A-matrix to be a matrix of 1x1 dimensions whilst P is a 1xn dimensional matrix. The D-matrix can be written...

a Block LU decomposition is a matrix decomposition of a block matrix into a lower block triangular matrix L and an upper block triangular matrix U. This...

the mathematical discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities...

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

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...

function fields. Typically Ω {\displaystyle \Omega } is chosen to be the block matrix Ω = [ 0 I n − I n 0 ] , {\displaystyle \Omega ={\begin{bmatrix}0&I_{...

Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms...

of matrices, numerical analysis, and statistics. It is defined for a block matrix. Suppose p, q are nonnegative integers such that p + q > 0, and suppose...

In mathematics, a block matrix pseudoinverse is a formula for the pseudoinverse of a partitioned matrix. This is useful for decomposing or approximating...

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

Look up Block, Blocks, block, blocked, or blocks in Wiktionary, the free dictionary. Block or blocked may refer to: Block programming, the result of a...

product, which takes a pair of matrices as input and produces a block matrix Standard matrix multiplication Given two vectors of size m × 1 {\displaystyle...

in a block matrix. It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the...

rotation matrix or differential rotation matrix is a matrix representing an infinitely small rotation. While a rotation matrix is an orthogonal matrix R T...

algebra, a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has zero entries...

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...

are the symplectic matrices. Suppose that the 2n-by-2n matrix A is written as the block matrix A = [ a b c d ] {\displaystyle A={\begin{bmatrix}a&b\\c&d\end{bmatrix}}}...

by the following trace diagram: More concretely, if we write out T in block matrix form after the decomposition into even and odd subspaces as follows,...

partition of an interval, partition of unity, partition of a matrix; see block matrix, and partition of the sum of squares in statistics problems, especially...

algebra, the Woodbury matrix identity – named after Max A. Woodbury – says that the inverse of a rank-k correction of some matrix can be computed by doing...

square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the...

In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and...

\Rightarrow \quad \det(\Lambda )=\pm 1} Writing the Minkowski metric as a block matrix, and the Lorentz transformation in the most general form, η = [ − 1 0...

"A block reflector is an orthogonal, symmetric matrix that reverses a subspace whose dimension may be greater than one." It is built out of many elementary...

of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known as "Jordan blocks". Each Jordan block contains...

efficiently as an adjacency list. A block-diagonal matrix consists of sub-matrices along its diagonal blocks. A block-diagonal matrix A has the form A = [ A 1 0...

two blocks with the two sites in the middle rather than just adding a single site to a block at each step as well as by using the density matrix to identify...