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Lect20 - Chapter 4 Linear Transformations Math1111 Linear...

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Chapter 4. Linear Transformations Math1111 Linear Transformations Motivation Recall: A function f from a set V to set W , written as f : V W , is an assignment of elements in V to elements in W such that (i) every element in V is sent to exactly one element in W , (ii) every element in V is assignment to some element in W . We input an element in V into f , then get an output in W
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Chapter 4. Linear Transformations Math1111 Linear Transformations Motivation Recall: A function f from a set V to set W , written as f : V W , is an assignment of elements in V to elements in W such that (i) every element in V is sent to exactly one element in W , (ii) every element in V is assignment to some element in W . Not allowed
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Chapter 4. Linear Transformations Math1111 Linear Transformations Motivation Recall: A function f from a set V to set W , written as f : V W , is an assignment of elements in V to elements in W such that (i) every element in V is sent to exactly one element in W , (ii) every element in V is assignment to some element in W . Allowed
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Chapter 4. Linear Transformations Math1111 Linear Transformations Motivation Recall: A function f from a set V to set W , written as f : V W , is an assignment of elements in V to elements in W such that (i) every element in V is sent to exactly one element in W , (ii) every element in V is assignment to some element in W . Not allowed
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Chapter 4. Linear Transformations Math1111 Linear Transformations Motivation Recall: A function f from a set V to set W , written as f : V W , is an assignment of elements in V to elements in W such that (i) every element in V is sent to exactly one element in W , (ii) every element in V is assignment to some element in W . Allowed
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Chapter 4. Linear Transformations Math1111 Linear Transformations Motivation Recall: A function f from a set V to set W , written as f : V W , is an assignment of elements in V to elements in W such that (i) every element in V is sent to exactly one element in W , (ii) every element in V is assignment to some element in W . A vector space is a set endowed with addition and scalar multiplication (and satisfying some axioms). Want to study functions preserve these operations.
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Chapter 4. Linear Transformations Math1111 Definitions & Examples Linear Transformation - Definition Definition Let V and W be vector spaces. A linear transformation L : V W is a function from V into W and satisfies L ( α v 1 + β v 2 ) = α L ( v 1 ) + β L ( v 2 ) for all v 1 , v 2 V and for all scalars α and β .
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Chapter 4. Linear Transformations Math1111 Definitions & Examples Linear Transformation - Definition Definition Let V and W be vector spaces. A linear transformation L : V W is a function from V into W and satisfies L ( α v 1 + β v 2 ) = α L ( v 1 ) + β L ( v 2 ) for all v 1 , v 2 V and for all scalars α and β .
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