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3A p1
Signed-off-by: szdytom <szdytom@qq.com>
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2
math.typ
2
math.typ
@ -1,6 +1,8 @@
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#let ee = "e"
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#let ee = "e"
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#let ii = "i"
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#let ii = "i"
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#let span = $op("span")$
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#let span = $op("span")$
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#let null = $op("null")$
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#let range = $op("range")$
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#let Poly = math.cal("P")
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#let Poly = math.cal("P")
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#let LinearMap = math.cal("L")
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#let LinearMap = math.cal("L")
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#let complexification(vv) = $vv_upright(C)$
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#let complexification(vv) = $vv_upright(C)$
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@ -1,5 +1,5 @@
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#import "../styles.typ": exercise_sol, note, tab, exercise_ref
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#import "../styles.typ": exercise_sol, note, tab, exercise_ref
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#import "../math.typ": Poly, LinearMap, ii, span, restricted, Permutation
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#import "../math.typ": Poly, LinearMap, ii, span, restricted
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#note[与原书一致,在本章中,如无其他说明,我们总是假定字母 $U$,$V$ 和 $W$ 都是 $FF$ 上的向量空间。]
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#note[与原书一致,在本章中,如无其他说明,我们总是假定字母 $U$,$V$ 和 $W$ 都是 $FF$ 上的向量空间。]
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@ -217,7 +217,7 @@
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]
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]
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#exercise_sol(type: "proof")[
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#exercise_sol(type: "proof")[
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给出一个例子:函数 $phi: RR^2 -> RR$,使得对于任意 $a in RR$ 和 $v in RR^2$,有
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给出一例:函数 $phi: RR^2 -> RR$,使得对于任意 $a in RR$ 和 $v in RR^2$,有
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$ phi(a v) = a phi(v) $
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$ phi(a v) = a phi(v) $
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@ -248,7 +248,7 @@
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]
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]
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#exercise_sol(type: "proof")[
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#exercise_sol(type: "proof")[
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给出一个例子:函数 $phi: CC -> CC$,使得对于任意 $w, z in CC$,有
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给出一例:函数 $phi: CC -> CC$,使得对于任意 $w, z in CC$,有
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$ phi(w + z) = phi(w) + phi(z) $
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$ phi(w + z) = phi(w) + phi(z) $
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17
sections/3B.typ
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17
sections/3B.typ
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#import "../styles.typ": exercise_sol, tab
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#import "../math.typ": null, range
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#exercise_sol(type: "answer")[
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给出一例:满足 $dim null T = 3$ 且 $dim range T = 2$ 的线性映射 $T$。
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][
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令
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$ T:& RR^5 -> RR^2 \ &(x_1, x_2, x_3, x_4, x_5) |-> (x_1, x_2) $
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#tab 根据定义
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$ range T &= RR^2 \
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null T &= {(0, 0, x, y, z) in RR^5 : x, y, z in RR} $
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#tab 于是 $dim null T = 3$ 且 $dim range T = 2$。
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]
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