How do you wrap your head around the poorly written chapter 9.3 in 'Contemporary Linear Algebra'?

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How do you wrap your head around the poorly written chapter 9.3in 'Contemporary Linear Algebra'?

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SOLUTION Here are some definitions are collected from different sources for chapter 93 in Contemporary Linear Algebra ie General Linear Transformations Isomorphism 1 Linear transformation Consider two linear spaces V and    See Answer
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