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  "body": "\n## Definition\n\nLet $F$ be a field and let $V$ be a vector space over $F$.\nAn *endomorphism* of $V$ is a [[linear map|0NRYHJPQG2]] $T \\colon V \\to V$.\nThe set of all endomorphisms of $V$ is written $\\End_F(V)$.\n\n## Remarks\n\nAn endomorphism is also called a *linear operator* on $V$.\nEndomorphisms can be composed with each other, so their powers $T^k$ and polynomials $p(T)$ are defined.\nUnder composition and addition, $\\End_F(V)$ is the [[algebra of endomorphisms|0E3X2G1ZQB]].\nEigenvalues, the trace and the determinant are defined for endomorphisms of finite-dimensional spaces.\n\n## Explanations\n\n### L1 human\n\nAn endomorphism maps a space into itself.\nSo we can apply it again and again, and compare a vector with its image.\nIn a basis, an endomorphism of an $n$-dimensional space is a square $n \\times n$ matrix.\n",
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