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13 October 2026
12 October 2026
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N 13:48 | vector space basis definition (Q2144) 6 changes hist +2,101 [Rongzhou (6×)] | |||
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13:48 (cur | prev) −13 Rongzhou talk contribs (Updated the item for vector space basis definition from Special:Update) | ||||
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11:17 (cur | prev) +2 Rongzhou talk contribs (Updated the item for vector space basis definition from Special:Update) | ||||
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07:32 (cur | prev) +59 Rongzhou talk contribs (Updated the item for vector space base definition from Special:Update) | ||||
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07:28 (cur | prev) +2 Rongzhou talk contribs (Updated the item for vector space base definition from Special:Update) | ||||
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07:27 (cur | prev) +236 Rongzhou talk contribs (Added content item: vector space base definition) | ||||
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07:27 (cur | prev) +1,815 Rongzhou talk contribs (Added content item: vector space base definition) | |||
| N 11:10 | Hyperplane diffhist +794 Rongzhou talk contribs (Created page with "Let $V$ be a vector space over $\mathbb{F}$. {{#content:Q2146}} == Properties == === Inner product space === If $V$ is an inner product space over $\mathbb{F}$ and $P$ is a hyperplane of dimension $k$. $\exists \vec w \in V, b \in \mathbb{F} \Rightarrow \forall \vec u \in P, \langle \vec w, \vec u \rangle =b$ Then $\vec w$ is called the '''normal vector''' of hyperplane $P$. If it is known that $P=\left\{ \vec p + \sum_{i=1}^{k} \lambda_{i}\vec v_{i}\, |\, \v...") | ||||
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11:03 | Vector subspace 2 changes hist −118 [Rongzhou (2×)] | |||
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11:03 (cur | prev) −136 Rongzhou talk contribs | ||||
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07:10 (cur | prev) +18 Rongzhou talk contribs | ||||
| N 08:42 | Linearly independent diffhist +594 Rongzhou talk contribs (Created page with "== Vectors == === Mathematical definition === A set of vectors $\{\vec{v}_1, \vec{v}_2, \dots, \vec{v}_n\}$ is '''linearly independent''' if $$ c_1 \vec{v}_1 + c_2 \vec{v}_2 + \cdots + c_n \vec{v}_n = \vec{0} $$ has no solution besides $$ c_1, c_2, \cdots, c_n = 0. $$ === Equivalent definition === Equivalently, it can be stated that if $$ \forall i,j \in \{1,n\} \vec v_i \neq \sum \lambda\vec v_j \\ \text{(no vector in the set can be written as a linear combinat...") | ||||