Vector spaces and the algebra of vectors are interesting and useful mathematical tools, but the justification for their importance is that they serve as the arena for the study of linear transformations. Linear transformations are the fundamental objects of study in a basic linear algebra course. In this central chapter we introduce linear transformations and study their most basic properties, postponing detailed numerical examples and their more intensive study to the following chapters.
KeywordsVector Space Linear Transformation Linear Subspace Linear Extension Dimension Formula
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