Suppose I have a matrix $H^{+} = (H^T H)^{-1} H^T$ where $H$ is a sparse matrix. Consider the case where only the sparsity pattern i.e. the zero elements of $H^{+}$ matrix is known, then would it be possible to infer the sparsity pattern or any other information of the $H$ matrix in either a deterministic or a probabilistic sense? Is there any reference or textbook that discusses such problems?
2026-02-22 21:43:43.1771796623
Matrix Sparsity Pattern
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