To prove: S is a sub-ring of M 2 ( ℂ ) where S = { [ x y − y ¯ x ¯ ] | x , y ∈ ℂ }

Question

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Answer 1

Question

Chapter 7.2, Problem 49E

(a)

To determine

To prove: S is a sub-ring of M2(ℂ) where S={[xy−y¯x¯]|x,y∈ℂ}

(b)

To determine

To prove: The mapping θ:H→S defined by θ(a+bi+cj+dk)=[a+bic+di−(c−di)a−bi]

is an isomorphism from the ring of quaternions H to S.

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Answer 2

Question

Chapter 7.2, Problem 49E

(a)

To determine

To prove: S is a sub-ring of M2(ℂ) where S={[xy−y¯x¯]|x,y∈ℂ}

(b)

To determine

To prove: The mapping θ:H→S defined by θ(a+bi+cj+dk)=[a+bic+di−(c−di)a−bi]

is an isomorphism from the ring of quaternions H to S.

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Answer 3

Question

Chapter 7.2, Problem 49E

(a)

To determine

To prove: S is a sub-ring of M2(ℂ) where S={[xy−y¯x¯]|x,y∈ℂ}

(b)

To determine

To prove: The mapping θ:H→S defined by θ(a+bi+cj+dk)=[a+bic+di−(c−di)a−bi]

is an isomorphism from the ring of quaternions H to S.

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Answer 4

Question

Chapter 7.2, Problem 49E

(a)

To determine

To prove: S is a sub-ring of M2(ℂ) where S={[xy−y¯x¯]|x,y∈ℂ}

(b)

To determine

To prove: The mapping θ:H→S defined by θ(a+bi+cj+dk)=[a+bic+di−(c−di)a−bi]

is an isomorphism from the ring of quaternions H to S.

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Answer 5

Chapter 7.2, Problem 49E

(a)

To determine

To prove: S is a sub-ring of M2(ℂ) where S={[xy−y¯x¯]|x,y∈ℂ}

(b)

To determine

To prove: The mapping θ:H→S defined by θ(a+bi+cj+dk)=[a+bic+di−(c−di)a−bi]

is an isomorphism from the ring of quaternions H to S.

Answer 6

Chapter 7.2, Problem 49E

(a)

To determine

To prove: S is a sub-ring of M2(ℂ) where S={[xy−y¯x¯]|x,y∈ℂ}

Answer 7

Chapter 7.2, Problem 49E

(a)

To determine

To prove: S is a sub-ring of M2(ℂ) where S={[xy−y¯x¯]|x,y∈ℂ}

Answer 8

(b)

To determine

To prove: The mapping θ:H→S defined by θ(a+bi+cj+dk)=[a+bic+di−(c−di)a−bi]

is an isomorphism from the ring of quaternions H to S.

Answer 9

(b)

To determine

To prove: The mapping θ:H→S defined by θ(a+bi+cj+dk)=[a+bic+di−(c−di)a−bi]

is an isomorphism from the ring of quaternions H to S.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

To prove: S is a sub-ring of M 2 ( ℂ ) where S = { [ x y − y ¯ x ¯ ] | x , y ∈ ℂ }

Solution Summary: The author explains that S is a sub-ring of M_2(C).

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To prove: S is a sub-ring of M2(ℂ) where S={[xy−y¯x¯]|x,y∈ℂ}

To prove: The mapping θ:H→S defined by θ(a+bi+cj+dk)=[a+bic+di−(c−di)a−bi]

is an isomorphism from the ring of quaternions H to S.

Want to see the full answer?

Chapter 7 Solutions

To prove: S is a sub-ring of M 2 ( ℂ ) where S = { [ x y − y ¯ x ¯ ] | x , y ∈ ℂ }

Solution Summary: The author explains that S is a sub-ring of M_2(C).

Videos

To prove: S is a sub-ring of M2(ℂ) where S={[xy−y¯x¯]|x,y∈ℂ}

To prove: The mapping θ:H→S defined by θ(a+bi+cj+dk)=[a+bic+di−(c−di)a−bi] is an isomorphism from the ring of quaternions H to S.

Want to see the full answer?

Chapter 7 Solutions

To prove: The mapping θ:H→S defined by θ(a+bi+cj+dk)=[a+bic+di−(c−di)a−bi]

is an isomorphism from the ring of quaternions H to S.