Lect20 - Chapter 4. Linear Transformations Math1111 Linear...

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Unformatted text preview: 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 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 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 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 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 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. 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 . 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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Lect20 - Chapter 4. Linear Transformations Math1111 Linear...

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