Lect22

# Lect22 - Chapter 4 Linear Transformations Math1111 Matrix...

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Chapter 4. Linear Transformations Math1111 Matrix Representations Theorem 4.2.2 Theorem 4.2.2 (Matrix Representation Theorem) Let L : V W be a linear transformation. Suppose that E = [ v 1 , ··· , v n ] , F = [ w 1 , ··· , w m ] are ordered bases for V and W respectively. Then there is an m × n matrices A such that [ L ( v )] F = A [ v ] E for every v V .

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Chapter 4. Linear Transformations Math1111 Matrix Representations Theorem 4.2.2 Theorem 4.2.2 (Matrix Representation Theorem) Let L : V W be a linear transformation. Suppose that E = [ v 1 , ··· , v n ] , F = [ w 1 , ··· , w m ] are ordered bases for V and W respectively. Then there is an m × n matrices A such that [ L ( v )] F = A [ v ] E for every v V . Remark The j th column a j of A is a j = [ L ( v j )] F .
Chapter 4. Linear Transformations Math1111 Matrix Representations Theorem 4.2.2 Theorem 4.2.2 (Matrix Representation Theorem) Let L : V W be a linear transformation. Suppose that E = [ v 1 , ··· , v n ] , F = [ w 1 , ··· , w m ] are ordered bases for V and W respectively. Then there is an m × n matrices A such that [ L ( v )] F = A [ v ] E for every v V . Remark The j th column a j of A is a j = [ L ( v j )] F . We call A the matrix representation of L relative to E and F .

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Math1111 Matrix Representations Proof of Theorem 4.2.2 Proof of Theorem 4.2.2. L
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Lect22 - Chapter 4 Linear Transformations Math1111 Matrix...

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