In linear algebra, a circulant matrix is a square matrix in which all rows are composed of the same elements and each row is rotated one element to the...

cyclic permutation of its vertices. The graph has an adjacency matrix that is a circulant matrix. The n vertices of the graph can be numbered from 0 to n −...

n × n Hadamard matrix is that n be a square number. A circulant matrix is manifestly regular, and therefore a circulant Hadamard matrix would have to be...

Skew-symmetric matrix (also called antisymmetric or antimetric) Centrosymmetric matrix Circulant matrix Covariance matrix Coxeter matrix GCD matrix Hankel matrix Hilbert...

Grudsky. Circulant matrix, a square Toeplitz matrix with the additional property that a i = a i + n {\displaystyle a_{i}=a_{i+n}} Hankel matrix, an "upside...

pseudoinverse trivially coincides with the matrix itself: A + = A . {\displaystyle A^{+}=A.} For a circulant matrix ⁠ C {\displaystyle C} ⁠, the singular value...

Multiplication operator Tridiagonal matrix Toeplitz matrix Toral Lie algebra Circulant matrix Proof: given the elementary matrix e i j {\displaystyle e_{ij}}...

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

roots of unity, the companion matrix and its transpose both reduce to Sylvester's cyclic shift matrix, a circulant matrix. Consider a polynomial p ( x...

kernel. Bateman transform Convolution kernel Circular convolution Circulant matrix Differential equations Kernel method List of transforms List of operators...

are indexed by field elements in the usual 0, 1, 2, … order, Q is a circulant matrix. That is, each row is obtained from the row above by cyclic permutation...

1&0&1&0&0&-\end{pmatrix}}} Which is circulant, i.e. each row is a cyclic shift of the previous row. Such a matrix is called a C W ( n , k ) {\displaystyle...

consequence of the circular convolution theorem is that the DFT matrix F diagonalizes any circulant matrix. A useful property of the DFT is that the inverse DFT...

their spatial interactions, then the interaction matrix is circulant. The eigenvalues of a circulant matrix are given by λ k = ∑ j = 0 N − 1 c j γ k j {\displaystyle...

determinant of Z. This is a consequence of Z being a circulant matrix and the theorem: If A is a circulant matrix in the class Ω(n,k) then if k > 3, perm(A) > |det...

matrix Tridiagonal matrix Block matrix Sparse matrix Hessenberg matrix Hessian matrix Vandermonde matrix Stochastic matrix Toeplitz matrix Circulant matrix...

m ≈ log ⁡ q {\displaystyle m\approx \log q} . Definition: The nega-circulant matrix of b {\displaystyle b} is defined as: for b = ∑ i = 0 n − 1 b i x i...

fractional integral and fractional derivative. Analog signal processing Circulant matrix Convolution for optical broad-beam responses in scattering media Convolution...

DFT matrix becomes a circulant matrix. Multiplying a data sequence with a circulant matrix is equivalent to the cyclic convolution with the matrix's row...

and h are ≤ N, it is reducible to matrix multiplication where the kernel of the integral transform is a circulant matrix. A case of great practical interest...

convolution or wrapped convolution. It results from multiplication of a skew circulant matrix, generated by vector a, with vector b. Circular convolution theorem...

lower-cost hardware—in particular, codes constructed such that the H matrix is a circulant matrix. Yet another way of constructing LDPC codes is to use finite...

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...

prime p Hermitian matrix Bloch sphere Discrete Fourier transform Generalized Clifford algebra Weyl–Brauer matrices Circulant matrix Shift operator Quantum...

used in numerical analysis. A circulant matrix is a matrix where every column is a cyclic shift of the previous one. Circulant matrices can be diagonalized...

the lepton masses are given by the squares of the eigenvalues of a circulant matrix with real eigenvalues, corresponding to the relation m n = μ [ 1 +...

[\mathbf {A} _{1}]_{p}} are pxp Jacket matrix, then [ A ] N {\displaystyle [A]_{N}} is a block circulant matrix if and only if A 0 A 1 r t + A 1 r t A...

diagonal matrix commutes with all other diagonal matrices. Circulant matrices commute. They form a commutative ring since the sum of two circulant matrices...

group. The roots of unity appear as entries of the eigenvectors of any circulant matrix; that is, matrices that are invariant under cyclic shifts, a fact that...

of order n, the matrix form of an element of K[C] acting on K[C] by multiplication takes a distinctive form known as a circulant matrix, in which each...