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  "body": "\n## Definition\n\nLet $F$ be a field, let $U$, $V$, $W$ be vector spaces over $F$, and let $S \\colon U \\to V$ and $T \\colon V \\to W$ be [[linear maps|0NRYHJPQG2]].\nThe *composition* of $T$ and $S$ is the map\n$$T \\circ S \\colon U \\to W, \\qquad (T \\circ S)(u) = T(S(u)).$$\n\n## Remarks\n\nThe composition of linear maps is linear.\nComposition is associative, and the identity maps are its identity elements.\nThe [[matrix of a composition is the product of the matrices|05Q1B7MH0M]], in the same order.\nComposition is not commutative: in general $T \\circ S \\ne S \\circ T$, even when both are defined.\n\n## Explanations\n\n### L1 human\n\nTo compose two linear maps, we apply one and then the other.\nWe write $T \\circ S$ for \"first $S$, then $T$\".\nMatrix multiplication is exactly this operation, written in coordinates.\n",
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