A Hankel matrix is a special type of square matrix where each ascending skew-diagonal from left to right is constant. This means that the elements in each diagonal line, starting from the bottom left to the top right, are the same. For example, a 3x3 Hankel matrix might look like this: \[ \beginbmatrix a & b & c \\ b & c & d \\ c & d & e \endbmatrix \] The first row contains the elements a, b, and c, while the subsequent rows are formed by shifting these elements to the right and down. Hankel matrices are often used in various fields such as signal processing, control theory, and numerical analysis. They can be useful for solving problems related to polynomial interpolation and time series analysis. Their unique structure allows for efficient algorithms to compute their properties, making them valuable in both theoretical and applied mathematics.