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  "body": "\n## Summary\n\nThe Hadamard product of two [[matrices|0VD9ZSWWJG]] of the same size is the matrix of the products of their corresponding entries.\nIt is also called the entrywise product or the Schur product.\nUnlike ordinary [[matrix multiplication|032Q9FB8MT]], it is commutative.\nThe Schur product theorem says that it keeps positive semidefinite matrices positive semidefinite.\n\n## Explanations\n\n### L1 human\n\nLay two tables of numbers of the same shape on top of each other.\nMultiply the two numbers in each cell, and write the result in that cell.\nFor example, the Hadamard product of $\\begin{pmatrix} 1 \u0026 2 \\\\ 3 \u0026 4 \\end{pmatrix}$ and $\\begin{pmatrix} 5 \u0026 6 \\\\ 7 \u0026 8 \\end{pmatrix}$ is $\\begin{pmatrix} 5 \u0026 12 \\\\ 21 \u0026 32 \\end{pmatrix}$.\nThis is different from the usual matrix product, which mixes rows with columns.\n",
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