Applied Mathematics 1411A/B Lecture Notes - Lecture 15: Transformation Matrix, Linear Map

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Matrix transformations from rn to rm (4. 9; pg. Recall: you are already familiar with functions from rn to r; this is a rule that associates with each element in a set a one and only one element in a set b. Definition: if f associates the element b with the element a, then we write is the value of f at a. A is the domain say that b is the image of a under f or that and the set b is called the codomain. The subset of b consisting of all possible values for f as a varies over a is called the range of f. Note: an important form of a transformation is: In the case where v = w, the. This is a transformation that maps a vector. If we denote this transformation by t, then mw. 2 jf are linear equations, you get a linear transformation: xaw.

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