$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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A vector space over a field $\mathbb{F}$ is a set of elements called vectors equipted with an addition and scalar multiplication such that
  1. communativity
  2. associativity
  3. existance of an additive identity
  4. exisitance of an additive inverse
exists. For scalar multiples, let $\vec{v}$ and $\vec{u}$ be vectors. We require
  1. 1\cdot \vec{v}=\vec{v}
  2. (\alpha\beta)\vec{v}=\alpha(\beta\vec{v})
  3. \alpha(\vec{u}+\vec{v})=\alpha\vec{u}+\alpha\vec{v}

Concepts

A vector space is basically a group with communitive addition. Do note that vector spaces can be made out of any set, such as sets of functions, sets of shapes, sets of numbers, as long as the way their addition and multiplication is defined satisfy the definition.

Used In

  • Subspace
  • Linear combination

Hypothesis

Coming soon

Results

Coming soon
A vector space over a field $\mathbb{F}$ is a set of elements called vectors equipted with an addition and scalar multiplication such that
  1. communativity
  2. associativity
  3. existance of an additive identity
  4. exisitance of an additive inverse
exists. For scalar multiples, let $\vec{v}$ and $\vec{u}$ be vectors. We require
  1. 1\cdot \vec{v}=\vec{v}
  2. (\alpha\beta)\vec{v}=\alpha(\beta\vec{v})
  3. \alpha(\vec{u}+\vec{v})=\alpha\vec{u}+\alpha\vec{v}

Concepts

A vector space is basically a group with communitive addition. Do note that vector spaces can be made out of any set, such as sets of functions, sets of shapes, sets of numbers, as long as the way their addition and multiplication is defined satisfy the definition.

Used In

  • Subspace
  • Linear combination

Hypothesis

Coming soon

Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results
FullPage
definition
concepts
used in
hypothesis
results
A vector space over a field $\mathbb{F}$ is a set of elements called vectors equipted with an addition and scalar multiplication such that
  1. communativity
  2. associativity
  3. existance of an additive identity
  4. exisitance of an additive inverse
exists. For scalar multiples, let $\vec{v}$ and $\vec{u}$ be vectors. We require
  1. 1\cdot \vec{v}=\vec{v}
  2. (\alpha\beta)\vec{v}=\alpha(\beta\vec{v})
  3. \alpha(\vec{u}+\vec{v})=\alpha\vec{u}+\alpha\vec{v}

Concepts

A vector space is basically a group with communitive addition. Do note that vector spaces can be made out of any set, such as sets of functions, sets of shapes, sets of numbers, as long as the way their addition and multiplication is defined satisfy the definition.

Used In

  • Subspace
  • Linear combination

Hypothesis

Coming soon

Results

Coming soon
A vector space over a field $\mathbb{F}$ is a set of elements called vectors equipted with an addition and scalar multiplication such that
  1. communativity
  2. associativity
  3. existance of an additive identity
  4. exisitance of an additive inverse
exists. For scalar multiples, let $\vec{v}$ and $\vec{u}$ be vectors. We require
  1. 1\cdot \vec{v}=\vec{v}
  2. (\alpha\beta)\vec{v}=\alpha(\beta\vec{v})
  3. \alpha(\vec{u}+\vec{v})=\alpha\vec{u}+\alpha\vec{v}

Concepts

A vector space is basically a group with communitive addition. Do note that vector spaces can be made out of any set, such as sets of functions, sets of shapes, sets of numbers, as long as the way their addition and multiplication is defined satisfy the definition.

Used In

  • Subspace
  • Linear combination

Hypothesis

Coming soon

Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results