Unformatted text preview: E for more details. When a linear mapping is de±ned in some way other than giving the coordinate polynomials, there is an easy way to ±nd its matrix representative. The proof of the following is outlined in Exercise 3 : Remark 4.1.1. The j th column of the matrix representative [ L ] of a linear mapping L : R 3 → R 3 is the coordinate column of L ( −→ e j ) , where { −→ e 1 , −→ e 2 , −→ e 3 } are the standard basis vectors for R 3 . 2 To avoid tortuous constructions or notations, we will work here with mappings of space to space; the analogues when the domain or target (or both) lives in the plane or on the line are straightforward....
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 Spring '08
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 Calculus, Transformations, representative, Howard Staunton, coordinate column

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