A Hankel matrix is a special type of matrix in which each ascending skew-diagonal from left to right is constant. This means that the elements of the matrix are determined by a sequence of numbers, where each element in the first column and the first row defines the rest of the matrix. For example, if the first column is a1, a2, a3 and the first row is b1, b2, b3, the matrix will have the form where each element is the sum of the corresponding row and column indices. Hankel matrices are used in various fields, including signal processing, control theory, and numerical analysis. They are particularly useful for solving problems related to polynomial interpolation and time series analysis. The properties of Hankel matrices allow for efficient computations, making them valuable in both theoretical and applied mathematics.