4.9 - MATH1850U/2050U: Chapter 4 cont. 1 GENERAL VECTOR...

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MATH1850U/2050U: Chapter 4 cont. .. 1 GENERAL VECTOR SPACES cont. .. Matrix Transformations from R n to R m (4.9; pg. 247) Recall: You are already familiar with functions from R n 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 ) ( a f b and say that b is the image of a under f or that ) ( a f is the value of f at a . A is the domain 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 . Example: Example: Definition: If V and W are vector spaces, and if f is a function with domain V and codomain W , then f is called a map or transformation from V to W and we say that f maps V to W . We denote this by writing W V f : . In the case where V = W , the transformation is called an operator on V . Note: An important form of a transformation is: ) , , , ( ) , , , ( ) , , , ( 2 1 2 1 2 2 2 1 1 1 n m m n n x x x f w x x x f w x x x f w This is a transformation that maps a vector ) , , , ( 2
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This note was uploaded on 10/12/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

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4.9 - MATH1850U/2050U: Chapter 4 cont. 1 GENERAL VECTOR...

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