Abstract: This chapter discusses the important concept of a linear transformation of a vector space. Matrices prove to be a powerful tool in the study of linear transformations of finite-dimensional vector spaces. They can be used to classify linear transformations according to certain equivalence relations that are based on the fundamental properties common to different linear transformations. In the chapter, U and V denote vector spaces of dimension n and m, respectively, over the field F, and T denotes a linear transformation of U into V. If T is a linear transformation of Rn into Rm, it is usually easier to find the matrix of T relative to ɛn and ɛm than with any other choice of bases, because the coordinates of a vector are the same as the components when working with the standard bases.
Publication Year: 1995
Publication Date: 1995-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
Access and Citation
Cited By Count: 3
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot