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Version 2 |
| Let $V$ be a vector space over a field $K$. |
Let $V$ be a vector space over a field $K$. A \emph{\PMlinkescapetext{linear functional}} on $V$ is a linear transformation $\phi:V\rightarrow K$, where $K$ is thought of as a one-dimensional vector space over itself. |
| A \emph{\PMlinkescapetext{linear functional}} on $V$ |
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| is a linear transformation $\phi\colon V\rightarrow K$, |
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| where $K$ is thought of as a one-dimensional vector space over itself. |
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| The collection of all linear functionals on $V$ |
The collection of all linear functionals on V can be made into a vector space by defining addition and scalar multiplication pointwise; it is called the dual space of V. |
| can be made into a vector space |
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| by defining addition and scalar multiplication pointwise; |
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| this vector space is called the dual space of $V$. |
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