Difference between revisions of "Dual vector space"
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Here a vector space is denoted as <math>(V,K)</math> where <math>K</math> is the field the vector space is over. | Here a vector space is denoted as <math>(V,K)</math> where <math>K</math> is the field the vector space is over. | ||
| − | The Dual space <math>V^*</math> is | + | |
| + | ==Definition== | ||
| + | Suppose {{M|V}} and {{M|W}} are two real [[Vector space|vector spaces]], we denote by <math>\text{Hom}(V,W)</math> ("Hom" is short for [[Homomorphism|homomorphism]]) the vector space of all linear maps <math>f:V\rightarrow W</math> | ||
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| + | The Dual space <math>V^*</math> or <math>V^\vee</math> is <math>\text{Hom}(V,\mathbb{R})</math>, that is the vector space of all real-valued linear functions on <math>V</math> | ||
{{Definition|Linear Algebra}} | {{Definition|Linear Algebra}} | ||
{{Todo}} | {{Todo}} | ||
Revision as of 05:43, 15 February 2015
Here a vector space is denoted as [math](V,K)[/math] where [math]K[/math] is the field the vector space is over.
Definition
Suppose [ilmath]V[/ilmath] and [ilmath]W[/ilmath] are two real vector spaces, we denote by [math]\text{Hom}(V,W)[/math] ("Hom" is short for homomorphism) the vector space of all linear maps [math]f:V\rightarrow W[/math]
The Dual space [math]V^*[/math] or [math]V^\vee[/math] is [math]\text{Hom}(V,\mathbb{R})[/math], that is the vector space of all real-valued linear functions on [math]V[/math]
TODO:
