向量（Vector）
定义
向量
是具有
n
n
n
个相互独立的维度的对象。
向量的模
：向量的长度。记作
∣
a
⃗
∣
|\vec{a}|
∣
a
∣
或
∥
a
⃗
∥
\|\vec{a}\|
∥
a
∥
。
单位向量
：长度为1的向量。
计算
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⋯
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)
T
\vec{x} = (x_1,x_2,\cdots,x_n)^T
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⋯
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)
T
y
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⋯
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)
T
\vec{y} = (y_1,y_2,\cdots,y_n)^T
y
=
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y
1
,
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⋯
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)
T
运算
例子
加减
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±
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=
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±
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⋯
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)
T
\vec{x}±\vec{y}=(x_1±y_1,\cdots,x_n±y_n)^T
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)
T
数乘
λ
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⃗
=
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λ
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λ
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)
T
λ\vec{x}=(λx_1,\cdots,λx_n)^T
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⋯
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λ
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)
T
内积
x
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∙
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=
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⃗
,
y
⃗
)
=
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⃗
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⋅
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∣
cos
θ
=
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y
=
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\vec{x} \bullet \vec{y} = (\vec{x},\vec{y}) = \vert\vec{x}\vert ⋅ \vert\vec{y}\vert \cosθ = x^Ty = y^Tx = x_1y_1 + x_2y_2 + \cdots + x_ny_n
x
∙
y
=
(
x
,
y
)
=
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⋅
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cos
θ
=
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外积
∣
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⋅
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=
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⋅
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sin
θ
\vert\vec{a} ⋅ \vec{b}\vert = \vert\vec{a}\vert ⋅ \vert\vec{b}\vert \sinθ
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⋅
b
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=
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⋅
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sin
θ
模
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2
\vert\vec{a}\vert = \|\vec{a}\| = \sqrt{\vec{a} \bullet \vec{a}} = \sqrt{x_1^2 + x_2^2 + \cdots + x_n^2}
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∥
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=
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2