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  "body": "\n## Definition\n\nLet $F$ be a field, let $V$ be a vector space over $F$, and let $T \\colon V \\to V$ be an endomorphism.\nLet $W$ be a $T$-[[invariant subspace|0ACX5QT8TE]] of $V$.\nThe *restriction* of $T$ to $W$ is the endomorphism\n$$T|_W \\colon W \\to W, \\qquad T|_W(w) = T(w).$$\n\n## Remarks\n\nThe map is well defined because $T(W) \\subseteq W$, and it is linear.\nIf $V$ is finite-dimensional, then the characteristic polynomial of $T|_W$ divides that of $T$.\nTake a basis of $V$ that extends a basis of $W$.\nIn this basis, the matrix of $T$ is block upper triangular, and its first diagonal block is the matrix of $T|_W$.\n\n## Explanations\n\n### L1 human\n\nIf a map keeps a subspace inside itself, then it is also a map of that subspace.\nThis smaller map is the restriction.\nIts eigenvalues are some of the eigenvalues of the original map.\n",
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