# Rank-two correction

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This is an update to an approximation of a matrix, notably to the hessian inverse, by adding a matrix of rank 2 to it. This generally takes the form of two rank-one updates: $LaTeX: \textstyle H^T = H + vv^T + uu^T,$ where $LaTeX: v$ and $LaTeX: u$ are linearly independent column vectors (so $LaTeX: \textstyle [vv^T + uu^T]$ is a rank 2 matrix).