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fix lint

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Signed-off-by: szdytom <szdytom@qq.com>
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方而静 2025-08-11 20:35:02 +08:00
parent fc2200bf0a
commit 66f20076e6
Signed by: szTom
GPG Key ID: 072D999D60C6473C
1 changed files with 8 additions and 8 deletions
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sections/3B.typ
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@ -460,7 +460,7 @@
$ dim range S T <= min{dim range S, dim range T} $
][
首先证明 $dim range S T <= dim range S$。设 $u in U$，则 $S T u = S (T u) in range S$，故 $range S T subset.eq range S$，即$dim range S T <= dim range S$。
首先证明 $dim range S T <= dim range S$。设 $u in U$，则 $S T u = S (T u) in range S$，故 $range S T subset.eq range S$，即 $dim range S T <= dim range S$。
#let SI = $restricted(S, I)$
#tab 现在证明 $dim range S T <= dim range T$。令 $I = range T$，则 $I$ 是 $V$ 的子空间。根据线性映射引理（原书3.4），存在 $SI in LinearMap(I, W)$，使得对于任意 $v in I$，有 $SI v = S v$。设 $u in U$，则 $T u in I$，因此 $S T u = SI (T u)$。故 $range S T = range SI T subset.eq range SI$，即 $dim range S T <= dim range SI$。