In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from...

designation "Hankel matrix" is often used for matrices satisfying the property in the second definition. Let A = (aij) be an n × n matrix. The first definition...

introducing the Hankel transform and the Hankel matrix. Hankel was born on 14 February 1839 in Halle, Germany. His father, Wilhelm Gottlieb Hankel, was a physicist...

dominating, each of which corresponds to exactly one Dyck word. The n×n Hankel matrix whose (i, j) entry is the Catalan number Ci+j−2 has determinant 1, regardless...

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

of. 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 down"...

submatrix is positive). The Hilbert matrix is an example of a Hankel matrix. It is also a specific example of a Cauchy matrix. The determinant can be expressed...

dimensional Hankel matrix and derive from this matrix an (A,B,C) realization of the LTI system. The key observation was that when the Hankel matrix is properly...

skew-symmetric matrix Hankel matrix, a square matrix in which each ascending skew-diagonal from left to right is constant Hasse–Witt matrix Hat matrix Hermitian...

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

be positive semi-definite. This is because a positive-semidefinite Hankel matrix corresponds to a linear functional Λ {\displaystyle \Lambda } such that...

Vandermonde matrix Stochastic matrix Toeplitz matrix Circulant matrix Hankel matrix (0,1)-matrix Matrix decomposition Cholesky decomposition LU decomposition QR...

the Hankel operator associated with this system. Hankel singular values also provide the optimal range of analog filters. Hankel matrix Hermann Hankel Hanzon...

Walsh–Hadamard transform) Fast wavelet transform Hankel transform, the determinant of the Hankel matrix Discrete Chebyshev transform Equivalent, up to a...

{\displaystyle A_{i}\in \mathbb {F} ^{n_{i}\times m_{i}}} . A matrix A {\displaystyle A} is block Hankel if A ( i , j ) = A ( k , l ) {\displaystyle A_{(i,j)}=A_{(k...

yields a system of equations, whose solution involves the inversion of a Hankel matrix. Let X 1 , X 2 , ⋯ {\displaystyle X_{1},X_{2},\cdots } be independent...

corresponding Hankel kernel on the nonnegative integers A = ( m 0 m 1 m 2 ⋯ m 1 m 2 m 3 ⋯ m 2 m 3 m 4 ⋯ ⋮ ⋮ ⋮ ⋱ ) {\displaystyle A=\left({\begin{matrix}m_{0}&m_{1}&m_{2}&\cdots...

cylindrical problem. In this domain total field is written in terms of Bessel and Hankel function solutions to the cylindrical Helmholtz equation. SMM method formulation...

characteristic polynomials for the principal submatrices of the shift operator. Hankel matrix Meurant, Gérard; Sommariva, Alvise (2014). "Fast variants of the Golub...

of the matrix depend on the product of the indexing monomials only (cf. Hankel matrices.) Moment matrices play an important role in polynomial fitting...

{\mathfrak {J}}^{-k}(b)_{n}=a_{n}=(\mathbf {E} +k)^{n}b_{0}.} Newton series Hankel matrix Möbius transform Stirling transform Euler summation Binomial QMF Riemann–Liouville...

lagged vectors of size L {\displaystyle L} . The matrix X {\displaystyle \mathbf {X} } is a Hankel matrix which means that X {\displaystyle \mathbf {X} }...

as the determinant of a catalecticant matrix (Eisenbud 1988), also called a Hankel matrix, that is a square matrix with constant (positive sloping) skew-diagonals...

(Annihilating filter-based low rank Hankel structured matrix completion approach). The data of the k-space matrix is numbered consecutively and is split...

&\ddots &\vdots \\m_{n}&m_{n+1}&m_{n+2}&\cdots &m_{2n}\end{matrix}}\right]} be a Hankel matrix, and Δ n ( 1 ) = [ m 1 m 2 m 3 ⋯ m n + 1 m 2 m 3 m 4 ⋯ m...

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...

1999. Professor Emeritus at Ritsumeikan APU University, Japan in 2020. Hankel Matrix Problems in the Airplane Control Systems, Research report to Boeing...

1 ) / 2 {\displaystyle (H_{n}^{0})=2^{n(n-1)/2}} where this is the Hankel matrix like H n {\displaystyle H_{n}} , but started with x 0 {\displaystyle...

coordinates, the spherical Bessel functions of the first kind and the spherical Hankel functions. Accordingly, there are two linearly independent sets of solutions...

of the penultimate emanant, which is the determinant of the n by n Hankel matrix with entries ai+jx + ai+j+1y for 0 ≤ i,j < n. Elliott, Edwin Bailey...