A Hankel matrix is a specific type of structured matrix that has the property that each ascending skew-diagonal from left to right is constant. In more formal terms, a Hankel matrix is defined by its entries being determined by a sequence of numbers; the entry in the \(i\)-th row and \(j\)-th column of the matrix is given by \(h_{i,j} = a_{i+j-1}\), where \(a\) is a sequence of numbers.
Articles by others on the same topic
A Hankel matrix has entries constant on each anti-diagonal: with indices starting at zero, . For example,This differs from a Toeplitz matrix, whose entries are constant along diagonals. A square Hankel matrix is symmetric, although it need not be positive semidefinite.
An important example uses moments of a positive measure on the real line, assuming the needed moments are finite. For a real coefficient vector ,so the moment Hankel matrix is positive semidefinite. Taking the point mass at gives and , of rank one. Thus the matrix pattern connects sequences, polynomials and moment problems.