Linear Algebra pp 199-225 | Cite as

Linear Transformations

Part of the Compact Textbooks in Mathematics book series (CTM)


In Chap.  1, we defined a matrix as a rectangular array of numbers (Definition  1.1.5). In this chapter, we give the mathematical definition of matrices through linear transformations. We will see that the multiplication of two matrices is equivalent to the composition of two linear transformations. One of the important properties of linear transformations is that they carry some algebraic properties from one vector space to another. Sometimes, this will provide us with the necessary knowledge of some vector spaces, without even studying them in detail, but by rather seeing them as the result of a linear transformation of other well-known vector spaces.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesUniversity of SharjahSharjahUnited Arab Emirates

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