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  "body": "\n## Summary\n\nA Hankel matrix is a matrix that is constant along each anti-diagonal, the lines that go from lower left to upper right.\nIts entry in row $i$ and column $j$ depends only on the sum $i + j$.\nHankel matrices appear for moment sequences, for the realisation of linear systems from their impulse responses, and in the theory of orthogonal polynomials.\nReversing the order of the rows turns a square Hankel matrix into a [[Toeplitz matrix|GKY2WSHE26]].\n\n## Explanations\n\n### L1 human\n\nTake a sequence of numbers $h_2, h_3, h_4, \\dots$ and write it into a square so that it runs along the anti-diagonals.\nFor example, $\\begin{pmatrix} 1 \u0026 2 \u0026 3 \\\\ 2 \u0026 3 \u0026 4 \\\\ 3 \u0026 4 \u0026 5 \\end{pmatrix}$ is Hankel, built from $1, 2, 3, 4, 5$.\nEach row is the row above it shifted one step to the left, with a new number at the end.\nA square Hankel matrix is always symmetric.\n",
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