Hilbert matrix information

In linear algebra, a Hilbert matrix, introduced by Hilbert (1894), is a square matrix with entries being the unit fractions H i j = 1 i + j − 1 . {\displaystyle...

this formulation is used is in Hilbert spaces. The finite-dimensional spectral theorem says that any symmetric matrix whose entries are real can be diagonalized...

sequences (they contain distinct elements). The Hilbert matrix is a special case of the Cauchy matrix, where x i − y j = i + j − 1. {\displaystyle x_{i}-y_{j}=i+j-1...

David Hilbert Foundations of geometry Hilbert C*-module Hilbert cube Hilbert curve Hilbert matrix Hilbert metric Hilbert–Mumford criterion Hilbert number...

In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional)...

{\displaystyle T} up to sign. The Hilbert matrix is an example of a Hankel matrix. The determinant of a Hankel matrix is called a catalecticant. Given...

norm on the matrix. Numerical methods for linear least squares Numerical stability Hilbert matrix Ill-posed problem Singular value Wilson matrix Belsley,...

{\displaystyle |1\rangle } in a two-dimensional Hilbert space, then the density operator is represented by the matrix ( ρ i j ) = ( ρ 00 ρ 01 ρ 10 ρ 11 ) = (...

Orthogonalization Parallelogram law Normal matrix, normal operator Orthogonal matrix Unitary matrix Semi-Hilbert space Diagonal matrix Eigenvector, eigenvalue, eigenfunction...

a Hilbert matrix. It has the unusual property that all elements in its inverse matrix are integers. Similarly, Richardson (2001) defined a matrix whose...

result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful...

square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is...

such norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication. Given a field...

scheduling Hilbert field Hilbert function Hilbert manifold Hilbert matrix Hilbert metric Hilbert modular form Hilbert modular variety Hilbert–Mumford criterion...

on finite-dimensional Hilbert spaces, so the notion of a unitary operator is a generalization of the notion of a unitary matrix. Orthogonal matrices are...

algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions;...

In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal...

linear algebra, a square matrix A {\displaystyle A}  is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists...

compact operator on Hilbert space is an extension of the concept of a matrix acting on a finite-dimensional vector space; in Hilbert space, compact operators...

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

transformation from Hilbert space C n {\displaystyle \mathbb {C} ^{n}} to C m , {\displaystyle \mathbb {C} ^{m},} then the matrix A H {\displaystyle \mathbf...

analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous...

state that has been found is projected into the Hilbert subspace for each block using a density matrix, hence the name. Thus, the relevant states for each...

In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*: A  normal ⟺ A ∗ A = A A ∗ . {\displaystyle A{\text{...

In mathematics, a symmetric matrix M {\displaystyle M} with real entries is positive-definite if the real number z T M z {\displaystyle z^{\operatorname...