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  "body": "\n## Description\n\nLet $F$ be a field and let $n \\ge 0$ be an integer.\nThe *coordinate space* $F^n$ is the set of $n$-tuples $(x_1, \\dots, x_n)$ with $x_i \\in F$.\nIt is a [[vector space|000AYPA9AJ]] over $F$ with the operations\n$$(x_1, \\dots, x_n) + (y_1, \\dots, y_n) = (x_1 + y_1, \\dots, x_n + y_n), \\qquad a(x_1, \\dots, x_n) = (ax_1, \\dots, ax_n).$$\nIts zero vector is $(0, \\dots, 0)$.\n\n## Remarks\n\nThe space $F^n$ has [[dimension|03GSZ8RTZJ]] $n$, with the [[standard basis|0V7ZD6P7RK]] $e_1, \\dots, e_n$.\nMore generally, for a set $I$, the set $F^I$ of all functions $I \\to F$ is a vector space with pointwise operations.\nEach $n$-dimensional vector space over $F$ is isomorphic to $F^n$.\nThe real spaces $\\R^2$ and $\\R^3$ model the plane and ordinary space.\n\n## Explanations\n\n### L1 human\n\nThe coordinate space $F^n$ is the space of lists of $n$ numbers.\nWe add two lists position by position, and we scale a list by scaling each entry.\nEvery finite-dimensional vector space looks like one of these spaces after we choose a basis.\n",
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