The Full Wiki

More info on Linear Algebra/Computing Linear Maps

Linear Algebra/Computing Linear Maps: Wikis


Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.


Up to date as of January 23, 2010

From Wikibooks, the open-content textbooks collection

< Linear Algebra

The prior section shows that a linear map is determined by its action on a basis. In fact, the equation

 h(\vec{v}) =h(c_1\cdot\vec{\beta}_1+\dots+c_n\cdot\vec{\beta}_n) =c_1\cdot h(\vec{\beta}_1)+\dots +c_n\cdot h(\vec{\beta}_n)

shows that, if we know the value of the map on the vectors in a basis, then we can compute the value of the map on any vector \vec{v} at all. We just need to find the c's to express \vec{v} with respect to the basis.

This section gives the scheme that computes, from the representation of a vector in the domain {\rm Rep}_{B}(\vec{v}), the representation of that vector's image in the codomain {\rm Rep}_{D}(h(\vec{v})), using the representations of  h(\vec{\beta}_1) , ...,  h(\vec{\beta}_n) .


Got something to say? Make a comment.
Your name
Your email address