Matrix representation is a method used by a computer language to store column-vector matrices of more than one dimension in memory. Fortran and C use...

a different matrix representation whose elements indicate whether vertex–edge pairs are incident or not, and its degree matrix, which contains information...

In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict...

produces a diagonal complex matrix representation of complex numbers, and setting b = d = 0 produces a real matrix representation. The norm of a quaternion...

of the corresponding matrix, and the conjugate of a complex number with the transpose of the matrix. The polar form representation of complex numbers explicitly...

Geohash Hilbert R-tree Linear algebra Locality preserving hashing Matrix representation Netto's theorem PH-tree Spatial index Discrete Global Grid Systems...

quaternionic matrix representation of g assigns a square matrix of quaternions ρ(g) to each element g of G such that ρ(e) is the identity matrix and ρ ( g...

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

a † {\displaystyle a^{\dagger }} to ψ 0 {\displaystyle \psi _{0}} . The matrix expression of the creation and annihilation operators of the quantum harmonic...

matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can...

&e_{n}\end{bmatrix}}S} with S an invertible n×n matrix. Now the new matrix representation for the symmetric bilinear form is given by A ′ = S T...

generalized by Richard Brauer from the 1940s to give modular representation theory, in which the matrix operators act on a vector space over a field K {\displaystyle...

These definitions are equivalent: if T {\displaystyle T}  has a matrix representation A = P D P − 1 {\displaystyle A=PDP^{-1}} as above, then the column...

Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a graph...

the representation theory of groups, in which elements of a group are represented by invertible matrices such that the group operation is matrix multiplication...

projection matrix that is not an orthogonal projection matrix is called an oblique projection matrix. The eigenvalues of a projection matrix must be 0...

scaling matrix. To scale an object by a vector v = (vx, vy, vz), each point p = (px, py, pz) would need to be multiplied with this scaling matrix: S v =...

group. A translation is an affine transformation with no fixed points. Matrix multiplications always have the origin as a fixed point. Nevertheless, there...

(V,h)} is called a Hermitian space. The matrix representation of a complex Hermitian form is a Hermitian matrix. A complex Hermitian form applied to a...

{\displaystyle m\times n} complex matrix A {\displaystyle \mathbf {A} } is an n × m {\displaystyle n\times m} matrix obtained by transposing A {\displaystyle...

In group theory, the lamplighter group L {\displaystyle L} is the restricted wreath product Z 2 ≀ Z {\displaystyle \mathbb {Z} _{2}\wr \mathbb {Z} } ....

physics areas. The representation of a rotation as a quaternion (4 numbers) is more compact than the representation as an orthogonal matrix (9 numbers). Furthermore...

|E|/|V|2 > 1/64, that is the adjacency list representation occupies more space than the adjacency matrix representation when d > 1/64. Thus a graph must be sparse...

]}} . The identity transformation is represented by the identity matrix [ 1 0 0 1 ] {\displaystyle {\bigl [}{\begin{smallmatrix}1&0\\0&1\end{smallmatrix}}{\bigr...

is this usual matrix one sees in Computer Graphics; however, a Givens rotation is simply a matrix as defined in the Matrix representation section above...

elements of the table are antisymmetric, making it almost a skew-symmetric matrix except for the elements on the main diagonal, as well as the row and column...

projection matrix. To project a vector onto the unit vector a = (ax, ay, az), it would need to be multiplied with this projection matrix: The vector...

In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes...

invertible, the square matrix A {\displaystyle A} appearing in its matrix representation is invertible. The matrix representation of the inverse transformation...

represented by the square matrix ( a b 0 a ) {\displaystyle {\begin{pmatrix}a&b\\0&a\end{pmatrix}}} . In this representation the matrix ( 0 1 0 0 ) {\displaystyle...