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  "body": "\n## Example\n\nLet $F$ be a field and let $m, n \\ge 1$.\nThe set $M_{m \\times n}(F)$ of $m \\times n$ [[matrices|0VD9ZSWWJG]] over $F$ is a [[vector space|000AYPA9AJ]] over $F$, with [[matrix addition|0Y7H3SAVA1]] and [[scalar multiplication|09V6DDACXR]].\nIts zero vector is the [[zero matrix|0ZTKJJDGR7]].\nThe matrices $E_{ij}$, with entry $1$ in position $(i, j)$ and $0$ elsewhere, form a basis, so $\\dim M_{m \\times n}(F) = mn$.\n\n## Remarks\n\nThe map that lists the entries of a matrix row by row is a linear isomorphism $M_{m \\times n}(F) \\to F^{mn}$.\nThe space $M_{m \\times n}(F)$ is isomorphic to the [[space of linear maps|0X9MBPP2Z3]] from $F^n$ to $F^m$.\nThe symmetric $n \\times n$ matrices form a subspace of dimension $n(n+1)/2$.\n\n## Explanations\n\n### L1 human\n\nMatrices of one fixed size can be added and scaled, so they form a vector space.\nA $2 \\times 2$ matrix holds four numbers, so this space has dimension $4$.\nIt is $F^4$ written as a square instead of a row.\n",
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