Difference between revisions of "Dual vector space"

Revision as of 05:43, 15 February 2015

Here a vector space is denoted as

$(V,K)$ where

$K$ is the field the vector space is over.

Suppose $V$ and $W$ are two real vector spaces, we denote by

$\text{Hom}(V,W)$ ("Hom" is short for homomorphism) the vector space of all linear maps

$f:V\rightarrow W$

The Dual space

$V^*$ or

$V^\vee$ is

$\text{Hom}(V,\mathbb{R})$ , that is the vector space of all real-valued linear functions on

$V$

TODO:

@@ Line 1: / Line 1: @@
 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 defined as follows:
+==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>
+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}}
 {{Todo}}