The Fundamental Theorem of Linear Algebra
The Fundamental Theorem of Linear Algebra
This chapter summarizes pictorially some of the linear algebraic foundations discussed thus far by revisiting the fundamental theorem of linear algebra, the unifying view of matrices, vectors, and their interactions. To make the discussion helpful and informal yet rigorous, and to complement the slightly more formal introduction of the basic ideas given in an earlier chapter, here the theorem’s pictorial representation is emphasized. The discussions cover the forward problem, when A ɛ ℝM×N maps an x ɛ ℝN from A’s domain onto b ɛ ℝM in A’s range, how A transforms x into b; and the inverse problem, discussed in detail in chapter 9, section 9.4.1.
Keywords: linear algebra, matrices, vectors, forward problem, inverse problem
Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.
