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

an invertible matrix is a square matrix that has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can...

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...

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

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

\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...

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...

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

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

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...

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...

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

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_{...

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...

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...

a special type of block matrix. In particular, the direct sum of square matrices is a block diagonal matrix. The adjacency matrix of the union of disjoint...

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...

Hamiltonian (quantum mechanics)) 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}}}...

the matrix. In spite of its name, the normal form for a given M is not entirely unique, as it is a block diagonal matrix formed of Jordan blocks, the...

algorithm for matrix multiplication? More unsolved problems in computer science In theoretical computer science, the computational complexity of matrix multiplication...

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...

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...

transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing...

real part. If we denote the 2n × n matrix whose columns form a basis of the corresponding subspace, in block-matrix notation, as ( U 1 , 1 U 2 , 1 ) {\displaystyle...

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...

vector comprising all those coordinates. The mass matrix M is the diagonal block matrix where in each block the diagonal elements are the mass of the corresponding...

\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...

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