- #1

- 153

- 11

- Homework Statement:
- Find eigenvalues & eigenvectors

- Relevant Equations:
- det(A-r*I) = 0

Thanks for your time.

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- Thread starter rugerts
- Start date

- #1

- 153

- 11

- Homework Statement:
- Find eigenvalues & eigenvectors

- Relevant Equations:
- det(A-r*I) = 0

Thanks for your time.

- #2

RPinPA

Science Advisor

Homework Helper

- 573

- 319

Multiply your ##\vec v## by the constant (1 + i). As you know, any multiple of an eigenvector is still an eigenvector of the same eigenvalue.

$$(1 + i) {2 \choose {2 - 2i}} = {{2 + 2i} \choose {2(1 - i)(1+i)}} = {{2+2i} \choose 4}$$

and similarly multiply ##\vec w## by the constant (1 - i).

$$(1 - i) {2 \choose {2 + 2i}} = {{2 - 2i} \choose {2(1 + i)(1-i)}} = {{2-2i} \choose 4}$$

Since the order is reversed, so are the eigenvalues with which each is associated.

- #3

Mark44

Mentor

- 34,934

- 6,698

- #4

- 153

- 11

Ahh, I see. Thank you

Multiply your ##\vec v## by the constant (1 + i). As you know, any multiple of an eigenvector is still an eigenvector of the same eigenvalue.

$$(1 + i) {2 \choose {2 - 2i}} = {{2 + 2i} \choose {2(1 - i)(1+i)}} = {{2+2i} \choose 4}$$

and similarly multiply ##\vec w## by the constant (1 - i).

$$(1 - i) {2 \choose {2 + 2i}} = {{2 - 2i} \choose {2(1 + i)(1-i)}} = {{2-2i} \choose 4}$$

Since the order is reversed, so are the eigenvalues with which each is associated.

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